Πρόχειρες Σημειώσεις Γ Λυκείου

&

.

Msc

2012

1 71.1 pi . . . . . . . . . . . . . . . . . . . . . . . . 7

1.1.1 . . . . . . . . . . . . . . . . . . . . . . . . 71.1.2 pi . . . . . . . . . . 81.1.3 pi . . . . . . . . . . . . . . . . . . . . . . . 91.1.4 pi . . . . . . . . . . . . 111.1.5 pi . . . . . . . . . . . . 12

1.2 - . . . . . . . . . . . . . . . . . . . . . 131.2.1 pi . . . . . . . . . . . . 151.2.2 pi . . . . . . . . 201.2.3 pi . . . . . . . . 211.2.4 pi pi . . . . . . . 221.2.5 pi . . . . . . . . . . . . . . 231.2.6 pi pi ... . . . . . . . 25

1.3 . . . . . . . . . . . . . . . . . . . . . . . . . . 251.3.1 L - C . . . . . . . . . . . . . . . . . . . . . . . . . . 251.3.2 . . . . . . . . . . . . . 271.3.3 pi . . . . . . . . . . . . . . . . . . . . . . . 281.3.4 . . . . . . . . . . . . . . . 29

1.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . 341.4.1 . . . . . . . . . . . . . . . . . . . . . . . 341.4.2 . . . . . . . . . . . . . . . . . . . . . . 38

1.5 . . . . . . . . . . . . . . . . . . . . . . . 401.5.1 . . . . . . . . . . . . . . . . . . . . . . . 401.5.2 . . . . . . . . . . . . . . . . . . . . . . 42

1.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

2 492.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492.3 . . . . . . . . . . . . . . 51

2.3.1 . . . . . . . . . . . . . . . . . 532.3.2 pi . . . . . . . . . . . 552.3.3 . . . . . . . . . . . . . . . . . . . 572.3.4 . . . . . . . . . . . . . . . . . . 60

2.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 612.4.1 pi . . . . . . . . . . . . . 62

2.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 652.5.1 . . . . . . . . . . . . . . . . . 66

2.6 . . . . . . . . . . . . . . . . . . . . . . . . 70

.

2.6.1 . . . . . . . . . . 712.7 - - . . . . . . . . . . . . . . . . . 73

2.7.1 . . . . . . . . . . . . . . . . . . . . . . . . 732.7.2 . . . . . . . . . . . . . . . . . . . . . . . . . 742.7.3 . . . . . . . . . . . . . . . . . . . . 76

3 793.1 . . . . . . . . . . . . . . . . . . . . 793.2 . . . . . . . . . . . . . . . . . . . . . . . . . 82

3.2.1 . . . . . . . . . . . . . . . . . 823.3 pi - pi . . . . . . . . . . . . . . . 863.4 pi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 903.5 . . . . . . . . . . . . . . . . 92

3.5.1 933.6 - . . . . . . . . . . . . . . . . . . . . 99

3.6.1 . . . . . . . . . . . . . . . . . . . . . 1023.7 . . . . . . . . . . . 104

3.7.1 . . . . . . . . . . 1043.7.2 pi . . . . . . . . . . . . . . . 1043.7.3 pi . . . . . 1043.7.4 . . . . . . . . . . . . . . . . . . 1053.7.5 . . . . . . . . . . . . . . . . 1053.7.6 - . . . . . . . . . 1063.7.7 . . . . . . . . . . . . . . 107

4 1094.1 ,

pi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1094.2

. . . . . . . . . . . . . . . . . . . . . . . . 1104.2.1 . . . . . . . . . . . . . . . . . . . . 1114.2.2 . . . . . . . . . . . . . . . . . . 1144.2.3 . . . . . . . . . . . . . . . . . . . . . 114

4.3 pi . . . . . . . . . 115

5 pi(Doppler) 1175.1 pi - pi . . . . . . . . . . . . . . . . . . 1175.2 pi - pi . . . . . . . . . . . . . . . . . 1185.3 pi - pi . . . . . . . . . . . . . . . . . 1195.4 pi . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

4

I 2011 - 2012 123

II 189

5

- . pi - pi .

pi pi - pi pi. pi, & pi , -pi & pi pi -.

pi , pi . pipi pi pi pipi . pipi 2011 - 2012. http ://perifysikhs.wordpress.com.

. , Msc

1

1.1 pi

1.1.1

pi pi pi - . , .. pi pi (T ), (f) ()

() pi pi pi pi pi . t pi , pi pi:

T =t

N(1.1)

pi 1 s.

(f ) pi pi pi t, pi t. :

f =N

t(1.2)

1 Hz 1 s1

pi , pi :

f =1

T(1.3)

() pi pipi :

=2pi

T= 2pif (1.4)

pi 2pisec. 1rad/sec.

.

1.1.2 pi

pi pi . pi pi . pipi pi (...).

pi pi pi pi , pi . pi pi t, pi :

x = A(t+ 0) (1.5)

pi . pi, pi pi pi . = t + 0 pi pi t . pi .

t = T - = 2pirad

pi 0 t = 0 . pi pi ( , , pi). :

0 0 < 2pi

pi :

=dx

dt= max(t+ 0) (1.6)

pi max = A . , pi pi (x = 0).

pi pi :

=d

dt= max(t+ 0) (1.7)

pi max = 2A pi . pi, (x = A).

(1.5),(1.6),(1.7) pi, pi pi pi. pipi pi pi

10

pi-pi (1.7) (1.5) :

= max(t) = 2A(t) = 2x (1.8)

pi pipi pi pi x pi , , pi pi pi pi .

-pi pi :

= A2 x2 (1.9)

pi pipi pi pi pi pi-

x = A(t) xA

= (t) x2

A2= 2(t)

= A(t)

A= (t)

2

2A2= 2(t)

pi pipi pipi :

x2

A2+

2

2A2= 2(t) + 2(t) = 1 =

A2 x2

1.1.3 pi

pipi pi pi-, pi pi pi 0 = 0.

pi pi pi pi pipi pi-

) t = 0 0.

) , pi pi pi.

) pi pi pi , pi .

11

.

1.1: pi -

1.2: -

12

1.3: pi -

) pi, pi :

pi pi pi .

pi .

) pi pi pi, - ( pi ) , pi pi pi, ( pi- )

1.1.4 pi

pi..1 pi pi t = 0 (x = +A). pi .

... x = A(t + 0) t = 0 +A = A(0) (0) = +1 0 = 2kpi + pi/2 0 = pi/2rad

pi..2 pi pi t = 0 pi pi pi . pi .

13

.

... x = A(t + 0) t = 0 x = 0 0 = A(0) (0) = 0 0 = 2kpi 0 = 2kpi+pi.

t = 0, = max (0) = 1 0 = pirad

pi..3 pi pi - t = 0 x = +A/2 pi pi. pi .

... x = A(t + 0) t = 0 x = +A/2 A/2 = A(0) (0) = 1/2 0 = 2kpi+pi/6 0 = 2kpi + pi pi/6.

t = 0, < 0 (0) < 0 0 = pi pi/6 = 5pi/6rad(2) * t = 0 pi > 0 0 = pi/6rad

1.1.5 pi

m pi , pi , pi . pi pi pi pi :

F = m (1.10)

(1.8) pipi

F = m2x (1.11) D = m2, pipi :

F = Dx (1.12) D pi

pi . pi (1.12) pi , pi :

1.4: pi14

pi pi ,

pi pi pi ,

pi pi pi pi pi

pi F = 0

(1.12) pi, pi pi pi pi pi 1.4

: (1.12) pi , pi . pi pi pi ,pi pi pi x pi pi pi pi pi . , pi , pi pi x pi pi pi (1.12).

- pi

pi D = m2 pipi : =

Dm

pi = 2piT

pipi :

T = 2pi

m

D(1.13)

pi pipi pi pi pi .

pi

pi (1.12),(1.5) pipi :

F = Fmax(t+ 0) (1.14), Fmax = DA

1.2 -

pi pi pi pi - pi pi .

15

.

1.5: -

pi pi -pi Hooke F = kl pi k ( pi ) l pi pi pi . F pi (l0)

(F) pipi pi pi-pi , pi pi pipi, pipi - pi , pipi .

pi pi pi , pi pi ;

- pi pi m

1 : , pi pi pi x pi pi

2 : pi pi.pi pi (F = 0)

3 : pi pi F . pi , pi -

16

pi pi x pi .

4 : F = Dx, D pi pi D.

5 : pi pi pi pi. pi pi pi (1.13) pi pi (1.5) 0

1.2.1 pi

pi pi pi pi . pi pi pi:

E =1

2DA2 (1.15)

pi pipi pipi pi pi , pi pi pi . pi.: pi pi .

& - -. pi pi :

K =1

2m2 (1.16)

U =1

2Dx2 (1.17)

(3

+6 C.>8145. F8; =82 @I=2 ' 81 =K5< I>.; CD6.; CD6

.

pi U = 12Dx2: -

pi , pipi F. - pi. (x) pipi pi , . pipi :

F = F = (Dx) = Dx pi

pi x pi pi. pi pi pi pi- F = f(x).

pi pipi pi pi pi- :

WF = E =1

2Dx2 (1.18)

K,U : 1.16 1.17 pi pi pi :

K =1

2m(max(t))

2 K = 12m2A22(t)

K = 12DA22(t) = E2(t) (1.19)

U =1

2D(A(t))2 U = 1

2DA2(t) = E2(t) (1.20)

18

pi 1.20 1.19 pipi pi pi pi . pi , pi :

1.6: E,K,U

: pi pi . :

K + U = E 12m2 +

1

2Dx2 = E

, pi = pi 1.15pi pipi pi :

() pi (x = 0) , - . E = Kmax =12m2max

19

.

() (x = A) , - E = Umax =12DA2

() pipi ( pi ..)

1

2m2 +

1

2Dx2 = E =

1

2DA2 =

1

2m2max (1.21)

pi pi pi , pi . pi pi- , pi pi pipi pi pi pi pi .

pi pi :

pi max = A :

E = Kmax 12DA2 =

1

2m2max A2 =

m

D2max A =

m

Dmax

pi D = m2 max = A

pi = A2 x2 :

1

2m2 +

1

2Dx2 = E =

1

2DA2 m2 = D(A2 x2)

D

m(A2 x2)

pi D = m2 = A2 x2

U = f(x), K = f(x) pi - pi :

U =1

2Dx2 A x +A

pi :

E = K + U K = E 12Dx2 A x +A (1.22)

pi pi pi .. pi 1.7:

20

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? &%- ( . $ ) *&

""""""#? ? ?$? * +,

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, &* ( 0&

'

.

-

.1-1'

.&

*2 &, &$, ,&$, &

1.7: E,K,U pi

U = f(), K = f() pi - pi :

K =1

2m2 max +max

pi :

E = K + U U = E 12m2 max +max (1.23)

pi pi pi 1.8:

: pipi pi pipi pi pi -, pi pi. pipi :

U =1

2k(l)2 (1.24)

, pi k l pi pi pi .

21

.

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? '%( ) * ?'

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???????!"# ? ? ?()* + , -& * + . ? -&(

? '%- ) . $ * ?'

""""""#? ? ?*+, *+,$? ? ??

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( (./0

) )* + , -& ! !* + ? ? ? * + (?! ! . ? + ( . ?( (

? ?(

( ./0 ./0? ?? ? ? + 1( (

*+,? '? ) 0'

*+,$? *+, '?? ' *+,? ?

.'

.

.1(1-

2

-

(

*+,'? '

1.8: E,K,U

pipi pipi -.

pi pi pi pi:

WF = U() U () (1.25)

pi . & . -pi : 1.1 - 1.108, 2.1 - 2.60, 1.131 - 1.146, 1.149- 1.156, 1.160, 1.161, 1.172, 1.174, 1.176, 1.178, 1.179, 1.180, 1.183, 1.184,1.186, 1.187, 1.188, 1.190

1.2.2 pi

pi pi pi pi pi. pi . pi pi .

pi dxdt

22

dx

dt= = A(t) (1.26)

ddt

d

dt= = 2A(t) (1.27)

dPdt

dP

dt= F = DA(t) (1.28)

- dKdt, dUdt

K + U = E d(K + U) = 0, =, dK = dU

dK

dt= dU

dt(1.29)

pi

dK

dt=dWFdt

=F dxdt

= F dKdt

= D x (1.30)

, (1.5),(1.6) pi-pi :

dK

dt= DA(t)A(t) dK

dt= DA

2

2(2t) (1.31)

dU

dt= +

DA2

2(2t) (1.32)

1.2.3 pi

. , . , pipi .

pipi pi pi :

x = A(t) = max(t) = max(t+ pi2 ) = pi

2 pi

.

23

.

pi - , pi pi pi t pi = pi

2, pi pi

pi : = 2pi

Tt t = T

4

pi pi = +max, pipi +A T

4.

pipi pi pi pi :

x = A(t) = max(t) = max(t+ pi) = pi pi

pi. pi -

pi , pi pi pi t pi = pi, pi pi pi :

= 2piT

t t = T2

pi pi = +max/2, pipi +A/2 T

2.

pi .

1.2.4 pi pi

pi pi pi -. pi : pi pi pi .

pi (1.9) :

()= () () x = (t) = t pi

. pi pi pi pi-

pi pi . pi pi pi (). pi pi 0.

pi . & . -pi : 1.162 - 1.165,1.169, 1.191, 1.192, 1.194,1.196, 1.197, 1.198, 1.200, 1.203, 1.33 - 1.70, 1.83 - 1.98, 1.101 - 1.108

24

& -

14

: 22 xA -= :.... :

2 2 2 2 2 2D A D x m A m xw w

2D=m

2 21 1 1E = K +U = m + = m +2 2 2

2 2 2 2A xw w - 2 =22 xA -=

3.

: yy ...

: = x = A x = At =t .

: ... , .

: x = At .

+

-

tx

1.9: pi pi

1.2.5 pi

pi pi pi pi pi . pi . pi , .

m1,m2 pi - ~1, ~2 . pi pi. .

pipi pi pi, pi pi pi . ~1, ~2, . :

~Po() = ~Po() m1~1 +m2~2 = m1~1 +m2~2 (1.33)

Eo() = Eo() K1 +K2 = K 1 +K 2 + Epi (1.34)pi Epi pi pi

. pipi (Ko() > Ko())

25

.

pipi pi pipi pi pi-pi .

pipi pi . ~1, ~2, (1.33) :

Ko() = Ko() K1 +K2 = K 1 +K 2 (1.35) pipi

. pi pi pi :

1: pi ... pi ( pi )

2: pi - pi pi pi pipi ( pi.. pi x pi pi pi ...)

3: pi pipi pi (1.33),(1.35) . pi (1.33 .

4: pi E = K + U .

5: pi pi pi

pi pipi pi pi -pi pi pi pi . pipi pi - . pipi pi , pi pi 4 5 .

pi pi (- ) , pi .

pi . & . -pi : 2.136, 2.138, 2.139, 2.140, 2.141,2.143,2.145, 2.146, 2.148, 2.149, 2,150, 2.151, 2.153, 2.154, 2.155, 2.156, 2.158, 2.159,2.160

26

1.2.6 pi pi ...

m1,m2 pi pi - , 1 = 2 = . pi pi :

D = (m1 +m2)2 2 = D

m1+m2 =

D

m1+m2

& -

31

U = :

U= 2 2 2

max max max1 1 1U + K = + = m + m = m 2 2 2

2 2 2max + = . ....

K=3U

2 2max max max

1 1U + K = U U + 3U = U 4U = U 4 D x = D 2 2

= 2

2 2 2 4 x = x = x4 2

... 1m 2m , ( 1 2 = = ), 1 2m = m + m .

21 1D = m 2

22D = m

( ) =21 2 1 2D = m + m D + D ... , D (D=K).

1 : 1: ... m. 2: (

AA

1m

2m

21 1D = m

22

2D = m

( ) K=21 2D = m + m

pi D1, D2 pi pipi :

D1 = m12, D2 = m2

2

pi pi , pi D = k

pi pi ( ), pi pi N . pipi pi N = 0 pi pi.

1.3

1.3.1 L - C

pi pi pi C, - pi pi L pi . - L-C.

pi pi V pi pi . pi Q UE pi . pi pi pi pi pi :

27

.

C =Q

V Q = CV (1.36)

UE =1

2CV 2 =

1

2

Q2

C(1.37)

t = 0, pi , pi pi pi . , pi pi , pi Lentz. pi pi pi pi pi Epi = Ldidt . VL = Epi = VC = qc , pi VC pi.

(4

(-4 -&!QMO)Q!* M+&+RM#*!)*

*81D7 1/?;=5147 /DB6H8A >H028;BF828.(.(2) =D6CI1D5. /26G1

5. =D68.?.=8A

1.3.2

pi pi (q) (i) pi pi. pipi pi , pi pi pi :

T = 2piLC (1.38)

pi pi pi :

q = Q(t+ 0) i = I(t+ 0) pi pipi

pi x - . pi Q pi ( pi ) I (pi -). pi = t + 0 pi 0 0 2pi.

pi pi pi pi pi , pi .

pipi pi t = 0 pi q = +Q pi i = 0 pi 0 = pi/2. pipi :

q = Q(t+pi

2) q = Q(t) (1.39)

i = I(t+

pi

2) q = I(t) (1.40)

pi I = Q, . ( ). (q) pi.

pipi pi t = 0 pi- (q = 0) pi pi I, pi 0 = 0. pipi :

q = Q(t) (1.41)

i = I(t) (1.42) pipi pipi , pi

pi pi pi. pi pi . pi pipi.

29

.

1.3.3 pi

pi pi - , pipi - pi (0 = pi/2. pi pipi pi.

1.11: -

pi

pi, pi pi pi t pi i q pi. i i , pi pi pi pi . .

i =dq

dt(1.43)

pi q, i

, - pi pi pi ( t = 0, q = +Q). pi (1.43), q , i > 0. pipi (1.39) , (1.61 , pi pi (1.11),(1.12)

pi ( dq

dt> 0)

30

1.12: -

(dqdt> 0) pi. pi pi pi

pi pi (i > 0) pi pi pi (i < 0).

pi . & . -pi : 5.1 - 5.11, 5.69, 5.70, 5.71, 5.72,5.73

1.3.4

pi pi t = 0. pipi pi, pipi pi pi, pi :

UE =1

2

Q2

C(1.44)

pi, pi pi pi pi . , pi pi pi pi pi. pi pi, pi pi , pi pi pi pi pi :

UB =1

2LI2 (1.45)

. pi pi , pi pi,

31

.

pi , pi pi . pi.

pipi pi pi pi , - :

E =1

2

Q2

C=

1

2LI2 (1.46)

pi pi (UE) pi pi (UB)pi pi :

UE =1

2

q2

C UB =

1

2Li2 (1.47)

UE,UB pi t = 0 pi 1.39 1.40 pipi pipi :

UE =1

2

(Q(t))2

C=

1

2

Q2

C2(t) UE = E2(t) (1.48)

UB =1

2L(I(t))2 = 1

2LI22(t) UB = E2(t) (1.49)

pi pipi pi pi pi pi pi pi pi , pi . .

pi pi pi pi pi. :

E = UE + UB 12

Q2

C=

1

2LI2 =

1

2

q2

C+

1

2Li2 (1.50)

pipi L C pi . pi pi L C :

pi Joule pi

pi pipi .

pi pi pi pipi :

32

1.13: E,UE, UB

pi I = Q

UB(max) = UE(max) 12LI2 =

1

2

Q2

C I2 = 1

LCQ2 I = Q (1.51)

pipi pi T = 2piLC = 1

LC

pi i = Q2 q2 (1.50) pi-pi :

1

2

Q2

C=

1

2

q2

C+

1

2Li2 Li2 = Q

2

C q

2

C i2 = 1

LC(Q2 q2)

i = Q2 q2 (1.52)

pi - UE UB q i. .

pi . & . -pi : 5.75 5.81, 5.83, 5.85, 5.86

pi pi-pi pi , pi - LC . pi :

33

.

pi pi dqdt

pipi :dq

dt= i (1.53)

pidVCdt

pi :

C =q

VC VC = 1

Cq dVC

dt=

1

C

dq

dt dVC

dt=

i

C(1.54)

pi i pi pi , - pi .

didt

pi pi (Lentz) pipi E = Ldidt , :di

dt= E

L

E = VL = VC = qC di

dt= q

LC di

dt= 2q (1.55)

pi pi dUEdt, dUBdt

pi pipi pi pi-pi :

E = UE + UB dE = 0 = dUE + dUB dUEdt

= dUBdt

(1.56)

pi PC pi PL pi. pipi :

dUEdt

= PC dUBdt

= PL (1.57)

dUEdt

= VCi =q

Ci (1.58)

pi . & . -pi : 5.87,5.88, 5.89, 5.91, 5.102, 5.103, 5.106,5.107, 5.109, 5.110, 5.112, 5.113, 5.114, 5.115, 5.116, 5.118, 5.119, 5.121

34

pipi pi... pi pi pi-pi t = 0 q, i pi pi pipi , pi pi pi pi- . pipi pi pi pi pipi pi pi pi. pi pi pipi :

pi pi pi () pi pi . pi pi Ohm :

I =E

R + r(1.59)

pi pi r . t = 0 pi pi pi-

UB = 12LI2 pi

pi . pipi pi t = 0, q = 0 i = +I

pi :

q = Q(t) (1.60)

i = I(t) (1.61)

pi pi pi pi pi q, i pi 0 = 0.

: pi . & . -pi : 5.93, 5.94, 5.95, 5.96, 5.97, 5.99, 5.100,5.123, 5.124, 5.126, 5.127, 5.128, 5.131, 5.132

35

.

L C mk pi pi LC pi . , pi pi .

- L Cpi x q i Q max = A I = Q U = 1

2Dx2

UE =12q2

C

K = 12m2 pi

UB =12Li2

k 1C

m pi pi L T = 2pi

mk

T = 2piLC

pi - pi pi L C pi pi .

1.4

1.4.1

pi pi - pi. , pi pi . pi ( ) pi - pi . pi , pi pi - pi pi. pi pi ,pi pi .

pi pi pi pi-. pipi pipi pi .

F = b (1.62) pi

36

pi . b pi pi -

pi pi pi pi . S.I. 1kg/s.pi pi pi b. , pi pi.

1.14: pi pi pi

pi pi -pi, pi pi pi-, pi pi pi x , , pi.

pi pi pipi - :

pi - . pi - pi pi -pi b. pi -, pi pi. pipi pi b pi pi , pi, - pi pi .

pi b, pi pi. b , pipi pi, pi -.

pi pi :

A = A0et (1.63)

pi A0 pi t = 0 = b2m . S.I. s1.

pipi pi pi (1.63)pipipi pi 50% pi pi - t1/2 pi pipi pi.

37

.

1.15:

A = A02

t1/2:

A02

= A0et1/2 1

2= et1/2 2 = et1/2 ln2 = t1/2 t1/2 = ln2

(1.64)

pipi pi -, pi pi .

38

1.16: pi pi

pi pipi . :

A = A0et, t = T, = 0, 1, 2, ...

pi pipi pipi pi-, pi , . , :

A0A1

=A1A2

=A2A3

= ... =AA+1

= . (1.65)

pi: pi t1 = T t2 = (T+1)T - :

AA+1

=A0e

(T )

A0e(T+1)= eT = .

pi pi pi:

E =1

2DA2 =

1

2D(A0e

t) E = 12DA20e

2t E = E0e2t (1.66)

pi, pi pi :

E0E1

=E1E2

=E2E3

= ... =EE+1

= . (1.67)

39

.

1.4.2

L C , pipi pi pi , pi pi . . pi pi pi .

pipi , pi - R, pi pi pi pi - pi b. pi, pi - pi . - pi - Joule, pi pi pi - . R, pi pi q pi t , , pi .

pi pi pipi pi :

pi R , , pi .

pi, pi , pi pi. pi . pi - .

pi pi pi.

pi pi pi :

Q = Q0et (1.68)

pi Q0 pi t = 0 = R

2L R L

pi pi. pipi pi pi .

pi pipi pi , pi :

40

1.17:

Q0Q1

=Q1Q2

= ... =QQ+1

= . (1.69)

41

.

pi pipi . pi pi (QR) pi :

QR = E0 E1 = 12

Q20C 1

2

Q2

C(1.70)

: pi . & . -pi : 6.1 - 6.38, 6.50, 6.51, 6.52, 6.53, 6.55, 6.56,6.58, 6.60, 6.61, 6.62, 6.63, 6.65, 6.66, 6.67, 6.68, 6.70

1.5

1.5.1

pi - . pi pi pi pi , . pi , , :

f0 =1

2pi

k

m(1.71)

pi . pi f0 ( pipi pipi f0. - .

f0 pi pipi , - .

pi ( ) - f pi f0 pipi :

=

20

(b

2m

)2, 0 =

D

m

pi F = b. pipi < 0 f < f0. pipi pi b pi ( ) pi f = f0.

42

pi , pipi - pi . .

pi , pi , pi pi pi. pi pi pipi pi . .:

, - pi , pipi pi -.

pi pi . - (f) - (f0). - pi - .

pi pi

pi f . , - f pi . pi , pi f0, pi pi pi , f . .

pi , pi .

pipi pi pi (b = 0), f = f0, pi pi. pi pi pi ( ) pi .

pi (b), pi pi pipipi pi pi. f pi f0. pi pipi pi pipi.

pi ,

pi , pi , -, pi .

43

.

1.18: pi pi

, pi pi- f, -. pipi - pi -pi - pi pi . pi pi - pi - pi pi. , - - pi, pi . pi, - (F) .

1.5.2

L C (pi.. pi pi pi ) :

f0 =1

2piLC

(1.72)

pi ( - LC), . , - (R 6= 0), pi - f0 ( pi pipi - ).pi , pi . pi pi pi , pi .

, pi f , . , pi pi , f f0

44

LC. pipi LC . pi pi pi I f , R.

pi - . pi pipi pi R , pi I -, pi pi pi pi pi , pi pi f0 .

1.19: pi pi

- pi -pi pi . pi L C . - - pi , f0 f .

: pi . & . -pi 7.1 - 7.29, 7.33-7.37,7.39, 7.40-7.43

1.6

pi , pi pipipi . pi , , pipi, pi , , pi pi pi . pi . pi pipi .

pi pi , pi . pi pi:

pi pi pi,

45

.

pi A1 A2 . pi :

x1 = A1(t) x2 = A2(t+ )

pi , pi - pi pi pi . :

x = x1 + x2 = A1(t) + A2(t+ )

1.20: pi pi-

pipi pi pi :

x = A(t+ ) (1.73)

pi

A =A21 + A

22 + 2A1A2 (1.74)

=A2

A1 + A2(1.75)

pi pipi pipi pi pi pi -, - pi x1 =A1(t).

pipi pi pi pipi .

pipi

() = 0, (1.74),(1.75) :

A =A1 + A2 + 2A1A2 =

(A1 + A2)2 A = A1 + A2

= 0 = 0rad pipi pi pi A1, A2 pi .

46

() = pirad, (1.74) :

A =A1 + A2 2A1A2 =

(A1 A2)2 A = |A1 A2|

(1.75) = 0 = pirad. pipi pi pi pi pi pi pi ( = 0, A1 > A2, = pi, A1 < A2).

pi pi -, pi , pi -. pi pi:

pi pi pi,

pi ,

1 2 .

pi pi :

x1 = A(1t) x2 = A(2t)

pi , pi pi pi pi- . :

x = x1 + x2 = A(1t) + A(2t) = A((1t) + (2t))

47

.

pipi :

x = 2A

(1 2

2t

)

(1 + 2

2t

)(1.76)

pi 1, 2 pi , pi pi pi :

pi

A = 2A(1 2

2t

)(1.77)

pi pi(1+2

2t). pi pi pi

pi , pi pi |A| = 0 |A| = 2A. pi

(1+2

2t)

=1 + 2

2' 1 ' 2 (1.78)

pi (1.76) :

x = A(t) (1.79)

pipi pi pi pipi pi pi |A| pi , , pi 2A. pi. :

pi pipi pi pi pi , pi - pi .

T ( -pi) pi, .

pi pi pi (1.77)pipi pi A :

2A

(1 2

2t

)= 0

48

1.21:

|1 2|2

t = (2+ 1)pi

2

pi = 0, 1, 2, ... = 0 = 1 , pi -

t1 t2 pi pi . pi pi :

T = t2 t1 = 3pi|1 2| pi

|1 2| T =2pi

|1 2| =2pi

2pi|f1 f2| pi pi :

T =1

|f1 f2| (1.80) pi

pi pi :

f =1

T= |f1 f2| (1.81)

49

.

: pi . & . -pi 8.1 - 8.44, 8.50 - 8.53, 8.55-8.59, 8.62 - 8.65, 8.67, 8.68, 8.70, 8.71,8.73-8.76, 8.78, 8.83-8.88, 8.90, 8.92, 8.94-8.98

50

2

2.1

pi .

pi, pi, : pi pi , pi pi .

. pi pi pi pi ,

pi pi -pi . , , -, pi pi pi pi . pi pi pi pi pi . pi ( . pi ), pi .

pi ,

( pi ) pi pi , pi pi pi . pipi , pi pi ( ), pi ... , pi pi pi pi , , pi .

pi pi , pi- .

2.2

, pi , :

.

, pi . ( , , pi) pi pi pi.

, pi . ( , , , ) c = 3 108m/s.

, :

, pi . .

pi , pi pi . pi pi .

, pi pi . pi .

2.1:

, :

, pi pi - . pi . - , pi - pi .

, pi pi pi . - , . pi . pi , .

, :

, pi pi pipi .

, pi .

52

2.2:

2.3

:

. pi, pi

pi , pi pi , f pi , pi - pi pi pi pi, pi pi. , , pi . :

() -pi pi . - pi t1 = T t2 = 2T , pi pi. -pi pi pi :

pi pi.

(f ) pi - .

, pi , pi pi pi .

() pi pi .

.

53

.

() pi . - pi, pi :

=x

t(2.1)

pi x pi pi t pi . pi pipi . pi pi .

.

2.3:

() pi - pi pi pi (2.1)t = T x = , :

=

T = f (2.2)

54

pi f . pi-pi . f pi pi pi . pi, pi , pi .

2.3.1

pi pi pi pi pi.

pi pi pi , pi pi f pi pi x (pi pi ) .

pi (x = 0) (=0) pi , pi pi pi y = 0 ( > 0). pi !

y = A(t) = A

(2pi

Tt

)(2.3)

pi pi pi .

pi pi pi ()=x pi pi :

t1 =x

(2.4)

pi t :

t t1 = t x

(2.5)

, pipi pi pi , pi pi :

y = A2pi

T

(t x

)= A2pi

(t

T xT

) y = A2pi

(t

T x

)(2.6)

(2.6) pi

55

.

x, pi pi , pi . pi = 2pi x

.

t pi pi (2.3), pi pi :

y = A

(2pi

Tt+

)= A

(2pi

Tt+ 2pi

x

) y = A2pi

(t

T+x

)(2.7)

pi x pi - pi .

, pi , pi pi . pi pi pi pi , pi pi pi xM pi :

pi pi pi

yM = A2pi

(t

T xM

)(2.8)

VM = A2pi

(t

T xM

)(2.9)

pi

M = 2 yM M = 2A2pi(t

T xM

)(2.10)

pipi pi - m pi . pipi , :

0 tT xM

0 t xM

(2.11)

, m pi pi pi D = m2 :

1

2Dy2 +

1

2mv2 =

1

2DA2 (2.12)

56

pi y pi pi pi v .

2.3.2 pi

pi pipi piy pi pi . pi t pi x . pi pi pi pipi pi . 2 pipi pi.

) pi - Ox, x = x1 pi :

y = A2pi

(t

T x1

)= f(t), t x1

pi y . pi

2.4: pi pi pi x1 .

pi . - pi , pi, pi.

) pi . t = t1, :

y = A2pi

(t1T x

)= f(x)

57

.

2.5: pi . pi , pi pi .

pi y Ox - pi x.

pi

1 : pi t = t1 y = f(x) pi pi .

2 : pi pi (x = t) pi ( /4).

3 : pi y (x = 0) t1,

58

pi 1 x = 0.

4 : pi pi pi pi pi , pi t1. t1 pi .

pi . & .pi : 9.1 -9.27, 9.70, 9.73, 9.74, 9.76, 9.78, 9.79, 9.81, 9.82,9.85, 9.87, 9.89, 9.90, 9.91 - 9.94, 9.96 - 9.98, 9.100 - 9.105, 9.107, 9.109

2.3.3

pi:

= 2pi

(t

T x

)(2.13)

(rad) . pi (2.13)pipi pi pi x pi pi t. Ox (x = x1) t t = t1 pi x pi pi .

pi 0. t pi pipi. , pi pi .

2.6: -

pi . pi - x = x1 :

M = 2pi

(t

T x1

), t x1

pipi pi - pi .

pi - t . d

pi .

59

.

. t1 t2 pi :

= 2pi

(t2T x1

) 2pi

(t1T x1

) = 2pi

Tt

2.7: -

t t1 :

M = 2pi

(t1T x

)

pi t1.

. - Oxpi pi pi xA xB pi -

. t :

A = 2pi

(t

T xA

)

B = 2pi

(t

T xB

) pi xB > xA A > B.

:

= 2pi

(t

T xA

) 2pi

(t

T xB

) = 2pix

pi pipi pi :

) x = , :

= 2pi

pi :

60

yA = A(A) yA = A(B + 2pi) = A(B) yA = yB: pi pi pi pipi , - pi pi pi . :

x = , = 1, 2, ...

pi pipi pipi : pi , pi

) x = (2+ 1)2, :

= (2+ 1)pi

pi,

yA = A(A) yA = A(B + (2+ 1)pi) = A(B) yA = yB

: pi pi pi pi pipi , pi - . :

x = (2+ 1)2, = 0, 1, 2, ...

2.8: pi pi , 2, 3, ..., pi pi

2, 3

2, 5

2, ....

61

.

pi . & .pi : 9.28 - 9.58, 9.122, 9.123, 9.126, 9.127, 9.128, 9.130 -9.136, 9.139, 9.140, 9.143 - 9.150, 9.153

2.3.4

(x = 0), pi pi, 0,

y = A(2pi

Tt+ 0)

:

y = A

(2pi

Tt 2pi

x+ 0

) y = A2pi

(t

T x

+02pi

)(2.14)

pipi pipi pi (2.6).

0 pi :

pi pi t = 0, pi pi t = 0 pi pi pi pi . pi t = 0 = 2pi

(tT x

+ 0

2pi

)= 0,

t = 0 ,

t = 0 pi v = vmax. pipi pi pi t = 0, pi pi ( pi ).

pipi pipi t = 0 (x = 0) v = +vmax.

pi pi 0 0 2pirad , pi pi pipi .

pi . & .pi : 9.156, 9.158, 9.160, 9.162, 9.163

62

2.4

pi . pi pi, pi pi :

pi pi pi pi , pi pi pi .

y = y1 + y2 + ...

pi :

pi pipi, , pi ,

-

: pi pi , pi .

pi pi pi- , pipi . pi , pi - pi pi pi .

pi pi pi .

63

.

2.4.1 pi

pi pi, . :

= .

, pipi . pi :

y1 = A(1t), y2 = A(2t+ )

pi :

= (2t+ ) 1t = (2 1)t+ pi , pipi

, : 2 1 = 0 2 =1 f2 = f1

pi ( = 0), pi pi. pi .

pi pi pi pi pi .

pi

pi pi 1 2 pipi pi , pi . pi pipi r1 r2 pi pi 1 2 .

pi pi pi , pi pi pi :

y1 = A2pi

(t

T r1

) y2 = A2pi

(t

T r2

)64

pi pi pi pipi, pi pi pi pi piy = y1 + y2. :

y = A2pi

(t

T r1

)+ A2pi

(t

T r2

) pipi :

y = 2A

(2pi r1 r2

2

)2pi

(t

T r1 + r2

2

)(2.15)

pi (2.15) pipi pi pi :

|A| = 2A|(

2pi r1 r22

)| (2.16)

= 2pi

(t

T r1 + r2

2

)(2.17)

pi (2.16) pipi pi pi pi pi .

pi pi pi pi pi pi pi 0 2. pi

. pi , =2, :

|(

2pi r1 r22

)| = 1

(2pi r1 r2

2

)= 1 2pi |r1 r2|

2= Npi

pipi pi pi pi pi pi pipi , pi 2.

|r1 r2| = N, N = 0, 1, 2, ... (2.18)

. pi , =0 :

(2pi r1 r2

2

)= 0 2pi |r1 r2|

2= (2N + 1)

pi

2

65

.

pipi pi pi pi pi pi pi pipi

2pi . pi

|r1 r2| = (2N + 1)2, N = 0, 1, 2, ... (2.19)

pi pi r1 r2=. pi. pi pi pi pi pi pi. pi .

pi ( ) pi (2.18). pi pi pi pi (=2).

pi pi ( )pi pi . pi pi pi pi (=0).

pi pi pi pipi, pi pi pi 0 < A < 2A

1 : pi 1 2, pi - A1 A2, pi pi pi pi (1.63), pi :

A =A21 + A

22 + 2A1A2 (2.20)

66

pi = 2pi |r1r2|

pi pi pi .

2 :pi pipi - pi pi . pipi pi , pi pi pi .

pi . & .pi : 10.1 - 10.35, 10.46, 10.48, 10.49, 10.51, 10.55, 10.57,10.58, 10.60, 10.61, 10.62, 10.65, 10.68 - 10.75, 10.77, 10.78, 10.80, 10.82,10.83, 10.84

2.5

pi, pi - pi ,pi pi .

2.9: .

pi pipi pi .

pi pi, pi pi .

pi pi pi pipi pi pi pi. pi pi , pi . pi pi pi pi , pi pi . pi , , pi pi pi. 3 , . pi pi pi, pi pi pi .

67

.

pi .

pipi :

pi pi pi .

pi pi pi. pi .

pi pi.

2.5.1

pi , pi . xx , pi pi pi pi.

pi pi (x = 0) , pi pi pi pi pi pi, y1 = y2 = A2piT t, pi pi pi :

y = y1 + y2 y = 2A2piTt

pi pi t = 0 pi pi pi ( = 0.

pi pi :

y1 = A2pi

(t

T+x

) y2 = A2pi

(t

T x

) pi pi pipi pi x pi t :

y = y1 + y2 = A2pi

(t

T+x

)+ A2pi

(t

T x

)

y = 2A(

2pix

)

(2pi

Tt

)(2.21)

(2.21) .

68

:

A = 2A(

2pix

)(2.22)

pi x .pi (2.21), (2.22) pi :

y = A(

2pi

Tt

)(2.23)

pi pi pipi :

pi pi

pi |A| , pi .

pi , pi , pi :

v = A(

2pi

Tt

) = 2A

(2pi

Tt

) pi:

. , A = 2A, :

2A2pix

= A 2pix

= 1 2pix

= k pi

x = k 2, k = 0, 1, 2, ... (2.24)

pi pi pi - , pi pi, pi 0,

2, 2

2, ..., k

2

pi =2. . pi - x

2.

. pi |A| , =0, :

2A2pix

= 0 2pix

= 0 2pix

= (2k + 1) pi

2

x = (2k + 1) 4, k = 0, 1, 2, ... (2.25)

69

.

pi pi pi - ,pi pi, pi

4, 3

4.5

4, (2k + 1)

4,

pi . . pi

2.

pi pi pi - pi pi

d = |x x| = |k 2 (2k + 1)

4| =

4

0 pi , pi pi pi . = t y = A(t).

.

pi pi -

2, , ,

pi pi pi , - . = pirad. pi pi = t+ pi y = A(t+ pi).

.

pi , pi

, pi pi . pi , pipi L :

70

L =

2, = 1, 2, ..

pipi pi pi pipi, pi

, pipi :

L =

4+

2, = 1, 2, ..

pi pi pi ,

pi pi . . pi, pi , ( ) pi. pi pi pipi pi pi pi t = T

2.

- pi

pi pi 2 pi

-

pi pi pi-

-

- . - pi - pi

2pi

pi pi pi pi -

pi - pi pi .

pi . & .pi : 11.1 - 11.36, 11.46 - 11.50, 11.52 - 11.59, 11.61, 11.63,11.64, 1.66 - 11.69, 11.71, 11.72, 11.75 - 11.79, 11.81

71

.

2.6

- pi. . .

pi . c = 3 108m/s

pi

pi - pi. pi pi pi . , pi ( ) pi - . , , pipi, pi pi pi pi . pi :

pi . pi pi pi. - pi pi pi pi , pi pi ,pi . pipi - pi . pi . pi pipi pi .

pi Maxwell - pi pipi :

, - pi .

pi ( c)

E

B= (2.26)

, pi , pi pi.

72

pi pi pi - pi x :

E = Emax2pi

(t

T x

)(2.27)

B = Bmax2pi

(t

T x

)(2.28)

pi Emax, Bmax pi .

pi :

2.10: pi pipi , x. ~B pi pi y ~E pi pi z

2.6.1

pi pi pi-. pi , pipi , pi pi pi. -pi pi pi . pi , - pi pi.

c :

c = fpi

.

73

.

pi pi - , . pi pi pipi.

. pi105m . pi , pi LC pi .

. pi 30cm 1mm pipi. pi . pi , .

pi . pi pi pi 1 mm 7 105m pipi. pipi pi pi pi pi . pi pi pi pi , pi pi pi pi-, .

. pi pi . - pi 400nm - 700nm ( 1nm = 109m). pi pi . pipi pi pi pi . :

700 630 nm 630 590 nm 590 560 nm 560 480 nm 480 440 nm 440 400 nm

pi . pi pi3, 8 107m 6 108m pipi. pi pi. pi pi , pi . pi pi. pi pi .

pi 108m 1013m pipi. pi pi pipi - . pi , .

74

. pi pipi pi - pi pi - pi . pi 1010m 1014m. pi - pi pi pi.

pi . & .pi : 12.1 - 12.16, 12.19 - 12.26

2.7 - -

2.7.1

pi pi , pi -

. . ) ) pi .

pipi pi pi pi, pi pi . , pi pi-, . pi . pi pi pi pipipi pi (), pi- . pi. -pi .

pipipi pi pi pi , pi . pipipi pi .

pipipi pi pipi pipi (pi) pi - (). pipi :

pipipi , pi pipi pipi ( pipi pipi)

pipi pi

pi = (2.29)

75

.

2.7.2

pi - pi , pi , - pipi pi , -. . pi : pi-, - pi , pi pi pi .

.

pi pi - . pi - - pi pipi - ().

pi , pi . c pi n .:

n =c

(n = 1) = c. (n > 1) c > pi. pipi :

pipipi , pi- , pipi , pipi.

, pipipi .:

pi

=n2n1 n1pi = n2 (2.30)

pipi Snell ()pi pi Snell

) pi 1 (n1) pi 2 (n2 > n1), pi

76

, pi pipi ( < pi).pi:

pi

=n2n1

> 1 pi > pi >

() pi pi 2 (n2) 1 (n1 < n2), pi pipi ( > pi).pi:

pi

=n2n1

< 1 pi < pi <

() pipipi pi- , . pi:

pi

=n2n1 n1pi = n2 n1 0 = n2 = 0 = 0

, pi pi

pi n1 pi n2 :

f , pi pi pipi pi pi . pi pi pi .

77

.

pi = c

n.

, .

f , pi = f pipi pi . pi ( ) pi , .

c = 0f , 0 . = f , . pipi pipi.

c

=0 n = 0

= 0

n(2.31)

pi n > 1 0 > .

2.7.3

pi pi pipipi pi, pi a na. pipipi pi pi b nb < na.

pi Snell pipi :

ab

=nbna

pi nb < na pipi b > a. pipi b pi pi

pipi a a pi pi pi -

pi ( ) crit.

pi pi Snell b = 90

o

crit90o

=nbna crit = nb

na

pipi pi , pi- pipipi pi

78

pi pi a. .

pi, , pi pi -, pi pi pi - , pi pi.

! pi pi pipi .

pi a na = n ( ) nb = 1 a :

crit =1

n(2.32)

pipi pi . pi.. crit = 41, 1o , crit = 24o. pi pi ( )pipi ! pi .

pi . & .pi : 13.1 - 13.50, 13.55 - 13.58, 13.60, 13.61, 13.62, 13.64,13.65, 13.67, 13.68, 13.70 - 13.77, 13.79, 13.80, 13.81, 13.83, 13.84, 13.87,13.88, 13.89

79

3

3.1

, pi R, pi . pi dt ds pi pi d.

~ t, -, pi pi ds pi dt.

dsd

.

pi

, pi, pi pi :

=2

R= 2 R (3.3)

pi pi . pi .

pi , .

pi pi ,pi pipi :

=

t= 0t 0 = t

.

, pi R. pi dt d~ d~ .

( pi) pi

, - pi.

pi ~ t , pi .

=d

dt(3.4)

pi pi , pi , . pi 1m/s2.

82

pi ~ - pi ~ pi ~ = ~ + ~ . pi =

2 +

2

pi

pi ~ t -, pi .

=d

dt(3.5)

pi d~. - pi 1rad/s2. pi 1rad/s2 1rad/s 1s.

= R pi :

d = R d ddt

= Rd

dt = R

pi pi pi , - .

pi pi pi, pi :

=

t= 0t 0

pi pipi pipi :

= 0 + t (3.6)

pi () - (t) pi pi- :

pi pi = t

83

.

pi pi t = 0 t pi pi pi pi . pi :

= 0t+1

2t

2 (3.7)

pipi pi ( < 0) pi-pi : = 0 | |t = 0t 12 | |t2.

pi .

s pi = ddt pi =

ddt

s = t = t

pi = 0 + t = 0 + ts = 0t+

12t

2 = 0t+12t

2

pi = 0 ||t = 0 | |ts = 0t 12 ||t2 = 0t 12 | |t2

3.2

3.2.1

pi , pi . , , pi . pi .

pi , pi pipi pi . , , pi , pi pi () ( pi).

pi , .

84

, .

3.1:

, pi pi pi:

pi

pi -pi pi pi .

, pi. pi ( pi) pi -

pi , pipi , pipi pi . pi pi pi . . - , pi pipipi. pi -pi pi pi pi .

pipi .

(cm) pi pi , pi .

, .

85

.

pi pi . 2 - :

~F = m~cm (3.8)

, pi , pipi . pi . pi pi . pi .

, pi .

pi , . pi .

pi pi pi pi () .

pi

pi pi pipi, -. pi , pi pi pi.

pi pi pi ():

. , pi , ~cm

86

. pi , pi pi pi pi pi pi pi

R , -, pi - pi . dx dt, pi pi d , pi ds, . pi pi, (dx = ds) pi :

d =ds

R ds = R d dx = R d

pi pipi pipi 1 , pi , .

x = R (3.9) (cm = dxdt )

( = ddt) pipi :

dx

dt= R

d

dt cm = R (3.10)

pipi pi pi - 2 . pi = R pi pipi cm = . pi- :

, , pi .

2 pi pi pipi . pi pipi pi pi pi - (~ = ~cm+~). pi pipi pipi :

:

o = cm

:

= cm = 0

87

.

:

z = cm + = 2cm

:

M =2cm +

2 =

2cm

pi pipi , pi , . dt dcm d. pi (cm = dcmdt ) pi ( =

ddt

) :

cm = R dcm = R d dcmdt

= R ddt cm = R (3.11)

pipi pi pi , 3 . pi = R pi pi pi , pipi cm =

, , pipi pi pi .

pi pi pi (~cm) , pi (~) pi (~).

pi . & .pi : 1.1 - 1.50, 1.55, 1.57, 1.58, 1.60, 1.61, 1.62, 1.65, 1.66,1.69, 1.72, 1.75, 1.77, 1.86 - 1.92, 1.94, 1.97, 1.98, 1.100, 1.101, 1.102, 1.105

3.3 pi - pi

pi

pi (~ ) pi pi .

)pi pi

, pi pi zz. ~F , pi

88

pipi pi pi pi pi l ().

pi pi pizz, ~ , pi :

pi

pi pi

F pi pi l pi pi, :

= F l (3.12)

pi 1N m.

pipi pi, , , (Fx) pi pipi (Fy) pi pi . pi :

= Fx l = Fl (3.13)

pi pi :

pi pi .

pi pi pi pi pi pi pi .

pi ( )pi , pi pi -pipi , pi pi pi .

)pi pi

pi pi , . , , pi , : pi pi

89

.

pi pi pipi pi . pipi pi pi pi pi pi pi.

pi pi , ~ , pi :

pipi pi pi

pi pi

F pi pi l pi . :

= F l

pi pi :

pi .

) pi

~F1 ~F2, pi - , pi . pi , pi , pi pi - pi pi (F1 = F2):

= F1x1 + F2x2 = F1(x1 + x2) = F1d pi -

~ , pi :

pipi ,

pi pi

~F1 pi pi d . :

= F1 d (3.14)

90

pi pipi pi pi pipi pipi pi pipi pi pipi .

pi . & .pi : 2.1 - 2.21,2.58, 2.59, 2.60, 2.62, 2.63, 2.65, 2.67

pi

, pi pi pipi. pi pipi :

)

~F = 0 (3.15)

pi pipi , pi - . pi ( = 0), pi pi ( ).

) pi pi pipi

= 0 (3.16)

pi pipi , pi - . pi ( = 0), pi pi .

pi -:

1: pi pi .

pi ( pi.. , , ). pi pi:

pi pi pi pipi, pipi pi .

2: pi x y pi .

91

.

3: pi pipi :

Fx = 0, Fy = 0, = 0

, pi pi . pipi pi pi , pi pi pipi.

4: pi pipi. - pi pi .

pi . & .pi : 2.22 - 2.55,2.81, 2.82, 2.85, 2.87, 2.90 - 2.99, 2.102,2.104, 2.105, 2.107, 2.108, 2.111, 2.113, 2.116, 2.118, 2.123.

3.4 pi

, pi pi - zz, pi pi . m1,m2, ...,m, pi pi . m1,m2, ...,m pi , r1, r2, ...r, .

pi I pi zz pi pi pi pi pipi pi. :

I = m1r21 +m2r

22 + ...mr

2 (3.17)

pi S.I. 1kg m2.

pi pi pipi pi - m, pi r, pi zz pi pi pipi pi :

I = mr2 (3.18)

:pi , pi pi - pi .

92

m1,m2, ...,m. m1 + m2 + ...m = M . pi pi R, pi R pi pi. pi :

I = m1r21 +m2r

22 + ...mr

2 = m1R

2 +m2R2 + ...mR

2

I = (m1 +m2 + ...m)R2 I = MR2

(Steiner)

pi Icm pi pi pi pi Ip pi pipi p, pi pi pi d pi pi pi, Steiner:

Icm pi pi pi pi , pi pi pi pi pi pi d pi pi pi pi pi pi pi pi d. :

Ip = Icm +Md2 (3.19)

:pi , pi pi pi pi- .

Steiner :

Ip = Icm +Md2 Ip = Icm +MR2 = MR2 +MR2 Ip = 2MR2

pi pipi pipi pi pi pi :

pi .

pi pi pi , pi .

pi pi.

93

.

3.2: pi pi , pi pi .

3.5

pi pi , pipi , , pipi . () pi (pi) :

~F = m~ (3.20)

pipi . .

, pi pi , pipi pi. (pi) pi ( pi) :

= I (3.21)

pipi -, pi pi :

pi pi pi , pipi pi , pi pi pi pi -.

pi 3.21 pi pi pi.

94

pi

pi pi 3.21 pipi pi pi , pi pi .

pi pi , , . :

m pi pi . - .

pi I pi pipi . .

, pi , pi - pi pi. , pi pi .

pi . & .pi : 3.1 - 3.25, 3.27, 3.28, 3.29, 3.32, 3.33, 3.36, 3.38

= I

. = 0 pi = 0. pi , pi pi pi . - , ( = 0), , ~, ~.( ).

. =. , pi =. , pi pi - pi, pi, .

3.5.1

pi pi pi , pi , pipi:

95

.

~F = 0, = 0 pi~F 6= 0, = 0 pi .

pi ~cm~F = 0, 6= 0 pi pi

pi pi , pi

~F 6= 0, 6= 0 ( pi - pi ~cm pi pi pi pi pi )

pi . & .pi :4.1 - 4.14,4.52, 4.53, 4.55, 4.56, 4.57, 4.60, 4.63, 4.64,4.66, 4.68, 4.69, 4.70

, pi ( , pi) pi pi :

() pi pi .

() -.

() , -.

, pi - :

pi pi pi .

pi pi .

pi :

~F = m

, pi :

= 0 + t, x = 0t+1

2t2

96

pi pi :

= I

pi - :

= 0 + t, = 0t+1

2t

2

pi pi pi pi - pi , . - pi pi x s = R = x. pi pi pipi - pipi pi pi pi pi pi pi :

cm = R

pi pipi .

pi . & .pi : 4.74, 4.76 - 4.82, 4.84, 4.86 - 4.89, 4.91, 4.92, 4.93

pi pi- - .

:

pi .

pi, :

~F = m~cm

, :

= I

pi pi pi - pi .

97

.

, pi pi pi -, pi- cm :

cm = R

pi pipi :

. -: pi pi , m R pi pi - . pi, pi pi . - pi . pi (~w) (~T ) , pi pi pi . pipi :

:

F = mcm mg T = mcm

:

= Icm TR = Icm

cm = R

pi . & .pi : 4.109, 4.111, 4.113, 4.120, 4.124, 4.134, 4.138, 4.144,4.146

. pipi: pipi pi (w) pi (T ), pi pi pi pi pi pi - . :

98

:

Fx = mcm mg T = mcm

:

= Icm TR = Icm

cm = R

pi pi :

pi pi (cm) pi pi , :

cm =mg T

m

pi pi, pi TR, pi , pi pi , pi pi cm R, pi cm = R .

, pi , pi pi pi , pi .

, pi pi , pi pi, pi , .

pi pipi pi , cm . pi pipi , pi pi .

99

.

pi pipi pi pi , cm . pi pipi , pi pi pi .

(~w), (~T ) - pi pi ( ~N ). pi pipi pi pi pi pi- :

0 T sN pi

, pipi :T < sN

T = sN , . pipi cm 6=R

pi pi pipi .

, R pi pi Icm pipi, pi pipi, pi , pi : pi pi cm pi -

: Fx = mcm = Icm cm = R

pi pi pi : x = 1

2cmt

2 t =

2xcm

pi pi - : cm = cmt cm =

2cmx

pi . & .pi - : 4.13 - 4.16, 4.19 - 4.44, 4.114, 4.116, 4.117, 4.119, 4.4.121,4.122, 4.127, 4.129, 4.130, 4.131, 4.132, 4.136, 4.137, 4.141, 4.143

. pi pi

pipi , L pi pi Icm = 112ML

2 pi pi pipi pi pi , pipi pi.

100

pi pi pi pi -, pi !

- pi pipi pipi :

(o) = I(o)

Steiner pi pi pi pi:

I(o) = Icm +M

(L

2

)2=

1

3ML2

pi pi pi pi :

(o) = MgL

2

pi ( = 0) pi pi MgL

2

pipi pi pi pi :

=3

2L

! . pi pi pi pi.

pi . & .pi - :4.150, 4.152, 4.153, 4.155, 4.156, 4.157, 4.158, 4.159, 4.161,4.163

3.6 -

, (~P ). , pi ~L.

) .

m pi pi - r, ~P ,pi .

101

.

, pi zzpi pi pipi , ~L pi :

pi

pi pi

p pi r . :

L = pr L = mr (3.22) S.I. 1kgm2/s. ,

(3.22) :L = m(r)r L = mr2 (3.23)

pi pi pi( = Fr). pi pi pi. pipi pi r pi pi (~), pi pipi pi.

) .

-pi pi pi pizz, pi pi, pi .

pi pi pi zz ~. m1,m2, ...,m, pi pi -. pi , pi zz ~ 1 = r1, 2 = r2, ..., = r.

:

L1 = m1r21, L2 = m2r

22, ... L = mr

2

102

pi pi. :

L = L1 + L2 + ...+ L L = m1r

21 +m2r

22 + ...+mr

2

L = (m1r21 +m2r

22 + ...+mr

2)

L = I

pi I = m1r21 +m2r22 + ...+mr2 pi , pi pi zz. pi :

pi pi pi ~L, pi :

,

pi pi

pi I , pi pi, pi . :

L = I (3.24)

-pi. , pi pi .

pi: pi pi pi pi pi pi pi. pi pi pi pi pi pi . pi , pi pi pi pi ( ).

)

pi pi .

pi pi ~L1, ~L2, ..., ~L ~L :

~L = ~L1 + ~L2 + ...+ ~L

103

.

pi -

pi pi pi pi pi dt d, pi pi (3.24) pipi :

L = I dL = Id dLdt

= Id

dt= I = dL

dt

: pi pi , pi pipi , .

pipi pi = I, pi .

pi, pi pi .

pi . 3 , - , -pi pi pi :

=dL

dt(3.25)

pi pi -, pi pi pi L , pi .

pi . & .pi - : 5.26 - 5.36, 5.60 - 5.63, 5.65, 5.67, 5.69, 5.70 - 5.72, 5.74,5.76, 5.79, 5.83, 5.84, 5.86, 5.87

3.6.1

pi = 0 :

=dL

dt= 0 L = .

: pi pi ( pi pi ) , ( pi ) pi .

104

pi = 0 - pi .

pi

pi pi pi . , - pi , pi pi , , -. :

~L = ~L (3.26)

pi pi pi pi pi pipi pi pipi .

I1 pi 1 I2 pi 2 pi pipi :

I11 = I22

pi pipi pi pi , . pi pi pi .

pi pi: pi pi pi, pi pi pi pi . , pi pi pipi , pi .

pi : pi 1,4 2,5 , pi . , pi , , pi - km. pi pi , pi . pi pi . pi pi

13000

s, pi pi 25 . pi . & .pi -

: 5.1 - 5.25, 5.37 - 5.49, 5.93, 5.95 - 5.99, 5.101, 5.102, 5.105,5.107, 5.108, 5.109, 5.111, 5.112

105

.

3.7 -

3.7.1

M pi ~. pi , m1,m2, ...,m pi ~. pi pi pi. :

K =1

2m1

2 +1

2m2

2 + ...+1

2m

2 K = 12M2 (3.27)

pipi pi pi , pi .

3.7.2 pi

pi ~ pi zz, pi .

pi , - m1,m2, ...,m, pi pi pi r1, r2, ..., r, pi pi. ~ 1 = r1, 2 = r2, ..., = r.

pi pi pi. -:

K =1

2m1

2 +1

2m2

2 + ...+1

2m

2 (3.28)

K =1

2m1

2r21 +1

2m2

2r22 + ...+1

2m

2r2

K =1

2(m1r

21 +m2r

22 + ...+mr

2)

2 K = 12I2

3.7.3 pi

~cm ~. . :

K = K +Kpi =1

2M2cm +

1

2Icm

2 (3.29)

106

pi M Icm pi , pi pi pi .

3.7.4

~F pi x pi pi W = ~F ~x. pi pi pi pi .

pi R, pi pipi pi pi pi , pi ~F - . pi d, pi pi ds = Rd. pi pi ds pi pi pi :

W = Fds dW = FRdpi = FR pi pi

pi pipi :

dW = d (3.30)

pi , pi W , pi d dW . pi pi pi :

W = (3.31)

W pi pi . pi pi pi pi pi.

3.7.5

pi pi ~F , pi pi pi pi . pi dt pi pi d, pi dW :

dW = d dWdt

= d

dt

107

.

pi dWdt

- (P ) . pi t :

P = (3.32)

S.I. 1Watt. pi :

P = F.

P pi pi W , pi pi pi pi t,pi t.

P =W

t(3.33)

3.7.6 -

pi pipi , pi pi pi 6= 0, pi pi pi pi pi K = 1

3I2.

pi pi pi pi . pipi pi pi pi - (....) :

K2 K1 = W 12I22

1

2I21 = W (3.34)

pi pipi pi - pipi pi pi. - . pi , , . pi pi .

t pi x pi pipi pi , :

x = R

108

pi pi pi pi- - .:

Kpi = W = (TR)

- . :

K = W = Wxx Tx K = W = Wxx TR

pipi pi :

Kpi + K = TR +Wxx TR K = Wxx

pi pipi pipi pi:

, t. .

pi - (....), pi pi pi .

3.7.7

.... pi pi ( pi.. , ). pipi pi pipi :

E = K +Kpi + U = o (3.35)

pi pipi , pipi pi - pipi pipi (U = 0). pi pi pi .

pi . & .pi - : 6.1 - 6.62, 6.90, 6.92, 6.93, 6.114, 6.116, 6.117, 6.118, 6.120.6.121, 6.122, 6.123, 6.124, 6.125, 6.127, 6.130, 6.131, 6.132, 6.133, 6.136, 6.137,6.139, 6.141, 6.143, 6.144, 6.145, 6.148, 6.149, 6.152, 6.155, 6.161, 6.167, 6.171,6.172, 6.146, 6.147, 6.153, 6.156, 6.159, 6.160, 6.163, 6.164, 6.165, 6.166,6.170, 6.174

109

.

-

pi: x : : = dx

dt : = d

dt

pi: = ddt

pi: = ddt: ~F pi : ~: m pi : I : :~F = m~ = I ~P = m~ L = I~F = d

~Pdt

= dLdt

: : ~F = 0, : ~P =. = 0, : L =. : piW = Fx W = : pi:P = F P = : pi:K = 1

2m2cm K =

12I2

- :

:

W = 12m22 12m21 W = 12I22 12I21

pi pi pipi pi pi . pi . pi .

110

4

pi . :

pi .

pi pi pi , pi pi pi (pi.. ). - .

pi pi, pi pi pi pi-. pi pi , pi pi , -pi pi, - .

-, pi pi - pi . pipi .

4.1 , pi .

() () ()

pi , pi - pi pi pi .

.

pi pi pi .

pi pi .

pi .:

~F =d~Podt

= 0 ~Po = ~Po(pi) = ~Po() , .

4.2 -.

pi pi pipi pi , . pi :

pi pi pi-, pi . pi pi pi pi -. pi , , , pi .

, pi pi .

pi pi pi pi pi . pi - , pi pi. pi pi

pi pi :

Ko(pi) = Ko()

112

pipi, pi - ( pi.. pi pi). pipi () pi .

pi - pi pi pi pi , pi. pi pi , pi pi pi. pi - pi

pipi pi - . pi . pi pi :

Ko(pi) Epi = Ko() Ko(pi) > Ko()pi Epi pi

pi.

4.2.1

m1 m2, pi pipi ~1 ~2. pi- ~1 ~2, pi - pi. pi pi pi - pi pi pipi.

~Po(pi) = ~Po() m11 +m22 = m11 +m22 (4.1)pi pi .

Ko(pi) = Ko() 12m1

21 +

1

2m2

22 =

1

2m1

1

2+

1

2m2

2

2 (4.2)

113

.

(4.1) :

m1(1 1) = m2(2 2)

(4.2) :

m1(21 12) = m2(22 22)

pipi :

1 121 12

=2 22

2 22 pipi 1 + 1 = 2 + 2 2 = 1 + 1 2

(4.1) pi 1 .

1 =m1 m2m1 +m2

1 +2m1

m1 +m22 (4.3)

2 =2m1

m1 +m21 +

m2 m1m1 +m2

2 (4.4)

pi pi - pi , pi pipi pi pipi .pipi pi, pi pi !

pipi

. m1 = m2 = mpi pipi (4.3),(4.4) pipi :

1 = 2 2 = 1

, pi , .

pipi pi pi pi , pi pipi.

. pi (2 = 0) pi (4.3),(4.4) pipi :

1 =m1 m2m1 +m2

1 (4.5)

114

2 =2m1

m1 +m21 (4.6)

pipi pi , (1 = 0) pi 2 = 1

pi

pi (m1

.

pi pi pi :

pi =y

=y

pi y = y = pipi pipi pi .

pi = (4.7) pi pi pi pipipi

pi pi. pi , pi pi pipi .

4.2.2

m1 m2 pi pi pipi ~1 ~2. ~1 ~2.

~Po(pi) = ~Po() m11 +m22 = m11 +m22pi pi .

Ko(pi) Epi = Ko() 12m1

21 +

1

2m2

22 Epi =

1

2m1

1

2+

1

2m2

2

2

pi Epi pi . pi ~V , . pi pipi pi pi pi . pi .

4.2.3

pipi pi , pi pi pi pipi. pi m1 m2 -. ~1 ~2. pi .

116

xOx

Po(pi)(x) = Po()(x) m11 = m11x +m22x

yOy

Po(pi)(y) = Po()(y) m11 = m11y m22y

Ko(pi) = Ko() 12m1

21 +

1

2m2

22 =

1

2m1

1

2+

1

2m2

2

2

pipi pipi , 4 - . pi pi ( pi ).

pi pi pi pi . pipi .

4.3 pi-

, pi t, pi , ( ) pi .

pi ~V Umax pi . pi .

pi pipi :

~Po(pi) = ~Po(t) m11 +m22 = m1V +m2V V = m11 +m22m1 +m2

pi pipi :

Ko(pi) = Ko(t) + Umax 12m1

21 +

1

2m2

22 =

1

2m1V

2 +1

2m2V

2 + Umax

pi Umax pi pi pi - pi.

117

.

pi . & .pi : 8.1 - 8.76, 8.102, 8.103, 8.104, 8.106, 8.118, 8.119,8.121, 8.126,8.127, 8.130, 8.131, 8.133, 8.134, 8.136, 8.139, 8.143, 8.144, 8.146,8.149, 8.151, 8.154, 8.156, 8.164, 8.168, 8.170, 8.173, 8.174

118

5

pi(Doppler)

pi . , pi pipi. pi pi .

, pi - pi , pi pi , pipi. . . pi , pi .

pi pipi pi pi Doppler:

Doppler pi, pi pi , pi pi pi pi pipi.

pi , , .

S pi, fS pi, ~S pi. pi pi-, fA pi pi ~A pi. ~S , ~A pi pi pi pi.

, pi pi -, . ~S ~A pi . pi pi pi .

5.1 pi - pi

pi pi S pi pipi pi fS. , pi :

= fS fS =

.

pi pi . pi- . pi pi . pi , pi pi pi , pi fA, pi . , pi pi, pi, pi pipipi.

fA = fS =

pipi pi pi

pi - pi pi - pi pi !

5.2 pi - pi

pi pi

pi pi pi - pi S ~A, pi . pipi pi pi pi pi- , pi , pi pi - pi -.

pi- ~A,B = ~A ~B, pi ~A,~B pi pi pi.

pipi pi pi pi pipi :

~ = ~ ~A = (A) = + A pi pi pipi pi pi : =

fS.

pi , pi pipi

, pi pi. pi pi :

fA =

= + A

= + A/fS

fA = + A

fS

120

pi + A > pipi pi pi - pi ( ) pi pi pi pipi (fA > fS).

pi pi

pi pi pi pi pi S ~A. pi pi pi pi pi, pi , pi pi . pipi:

~ = ~ ~A = A = A pipi pi pi :

fA =

= A

= A/fS

fA = A

fS

pi A < pipi pi pi - pi () pi pi pi pipi (fA < fS).

5.3 pi - pi

pi pi

pi pi S ~S, pi pi . - , pi pi pi pi. pi = fS .pi pi pi pipi , pi pi pi pi pi pipi.

pi A pi pi . pi pipi . pi pipi pi pi. pi pi x = ST pi pi. pi pi ST . pi A pi pi .

121

.

pi pi :

fA =

A=

ST =

fS S

fS

fA = S fS

pi S < pipi pi pi - pi () pi pi pi pipi (fA > fS).

pi pi

pi pi S pi ~S pi pi- , pi pi pipi pi pi , pi pi pi ST . pi pi +ST . pi pi :

fA =

A=

+ ST=

fS

+ SfS

fA = + S

fS

pi + S > pipi pi pi - pi () pi pi pi pipi (fA < fS).

5.4 pi

pi pi , pi pi pi pi pipi pipi.

fA = A S fS (5.1)

pi pi pipi : pi pi pi,

pi , pi pi pi . pi!

pi (+) - pi pi pi pi (-) pi pipi pi pi.

pi pi (-) pi pi pi pi (+) pi pi pipi pi.

122

pipi

Doppler pi pi-, pi (tA). pi pi pipi tS. pi :

fA =NAtA

fS =NStS

pi pi pipi (NS) pi pi (NA). pipi :

fAtA = fStS tA = fSfA

tS

, pi pi , fA = fS, .

pi pi pi pi pi pi

pi ~S pi pi pi - pi, pipi pi pi pipi -. pi pi pi pi pi - pi pi - pi .

pi pi

pi pi , pi pi .

pipi pi S(t) . pi pi pi S = A(t+ 0).

pipi pi - A(t). pi pi pi S = St

pi . & .pi : 9.1 - 9.45, 9.50, 9.51, 9.53, 9.54, 9.56, 9.57, 9.58, 9.61,9.62, 9.63, 9.65, 9.67, 9.68, 9.71

123

.

124

I

2011 - 2012

2011-2012

1 pi

:pi: : : 3

1 1.1 1.4 pi pi (4 5 = 20 )

1.1. pi , pi pi - pi , x =A(t)., :

() = A(t)

() = A(t)() = A(t)

() = A(t)

1.2. pi ,pi pi . pi pipi 3 ,

() pi pipi

() pi pipi

() pi pi

() pi pi

1.3 m pi pi pi .pi pi pi pi D. :

() pi

() pi

() pipi

() pi

perifysikhs.wordpress.com .

2011-2012

1.4 pi pi T = 4s. pi f :

() 4 Hz

() 2 Hz

() 0,5 Hz

() 0,25 Hz

1.5 () pi () pi. (5 1 = 5 )

() pi pi pi .

() pi pi-.

() .. pipi F = Dx.

() .. pi pi

() pi , pi < 0 pi < 0. pi pi pi (x = 0) .

22.1 pi pi pi pi pi- x pi pi .

() pi x = +0, 1m U pi :

) K = U) K = 3U K = 2U

pi pi pi .(3+4=7)


2011-2012

() pi F pi x pi pi -pi :

) F = 200x(S.I.)) F = 100x(S.I.)) F = 400x(S.I.)

pi pi .(3+3 = 6)

2.2. pi . - pi , U , .

12-16 -

12.

.

, U ,

.

U, 120 .

:

) 30 Hz.

) 2 z.

) 0,5 Hz.

( )

:

.

U t K t, ,

U. 4

, 4 .

120N 30

4= = .

:N 30 30 f

t 1 min 60 s= = =

f 0,5 Hz= .

U , 120 pi. :

) 30 Hz.


2011-2012

) 2 Hz.

) 0,5 Hz.

pi pi pi . (3+3 = 6)

2.3. k, pi pi , m pi - pi d/2 pi . pi pi, pi d. , pi pi :

() F/Fpi = 1/3

() F/Fpi = 1/2

() F/Fpi = 2

() F/Fpi = 3

pi pi pi. pi . (3+3 = 6 )

3 1 kg . t =0 pi x =

2m,

pi ( = 3U). pi pi F = 16x(S.I.) :

() , t = 0.

() pi 0


2011-2012

() pi .

() t = pi24s.

() pi pipi pi.

(4+4+4+7+6 )

4 k = 100N/m

m = 1kg . pi t0 = 0 . pi pi .

() pi pi pipi pi pi .

() pi pi pi - pi pi .

() pi pi pi pi pi pi.

() t = 0 pi pi 50% pi pi pi . .

g = 10m/s2.

(5+8+5+7 )

pi

pi

!!!

pi !


2011-2012

2 pi

:pi: : : 3

1 1.1 1.4 pi pi (4 5 = 20 )

1.1. m pi pi k, pi pi pi , pi pi . pi pi , pi :

() 4

() 2

() /2

()

1.2. .. . pi - :

() U = E/3

() U = K

() 4U = 3E

() U = 3E

1.3 .. t1 pi -pi pi ( < 0) . t1 :

() (x < 0)

() ( < 0)

() pi

()


2011-2012

1.4 pi . :

() pi

()

()

()

1.5 () pi () pi. (5 1 = 5 )

() pi pi .., pi pi pi pi .

() pi pi x1 = A/2 pi pi pi pi x2 = A.

() t = 0 pi pi , .

() pi ... pi, pi .

() () pi ... pi (x) pi pi .

22.1 .. . pi pi - pi , pi pi pi pi pi . (5 )

2.2. pi pi pi pi -pi pi pi .

pi :

() = 4pi(10pit) (S.I.)

() = 4pi(10t+ pi2) (S.I.)

() = 4pi(10pit+ pi2) (S.I.)

pi pi pi . (2+3 = 5)


2011-2012

-0,4

0

0,4

0 0,1 0,2

x(m)

t(s)

5 . 5. . .

. , b.

. , .

. ,

. b .

5

2

1. x1 = A1(t) x2= A2(t

+3).

1=2J 2=4,5J, : .=6,5J .E=2,5J .E=9,5J

3 .

7 2. . : . = 4(10t) (S.I.)

. = 4(10t+2) (S.I.)

. = 4(10t+2) (S.I.)

2 .

4 3. . t1 .

16

0A :

2.3. pi - (1) (2) , pi pi .

( 5)

2. , .

( 10)

. - (1) (2) , . ) E1 (1) E2 (2) :i) E1 = 2E2ii) E1 = 4E2iii) E2 = 4E1iv) E1 = E2

( 7)

) (1) (2) , :i) F1 max( ) = F2 max( )ii) F1 max( ) = 2F2 max( )iii) F1 max( ) = 4F2 max( )iv) F1 max( ) = 2 F2 max( )

( 8)

3 A = 10cm T = 6s . t = 0 .) ) -) , x = 5 3cm) ;

( 3+5+7+10=25)

4

x = 2 2 t +4

( x cm , t s ). :

)

) 2

() E1 (1) E2 (2)pi :

(i) E1 = 2E2(ii) E1 = E2(iii) E2 = 4E1(iv) E1 = 4E2

pi pi pi. pi . (3+4 = 7 )

() pi pi (1) (2) , pi :

(i) F1(max) = F2(max)


2011-2012

(ii) F1(max) = 2F2(max)(iii) F1(max) =

2F2(max)

(iv) F1(max) = 4F2(max)

pi pi pi. pi . (3+5 = 8 )

3 m = 1kg - k = 100N/m, pi pi . pi. pi |0| =

3m/s, pi pi t0 = 0.

() pi pi pi , pipi pi pi.

() pi pi pi t0 = 0 pi pi pi

() pi t, pi pi 0, 1m pi pi.

g = 10m/s2.

(10+10+5 )

4 m1 = 3kg k = 400N/m , pi . pi pipi pi pi A = 0, 4m. t0 = 0 pi. t = T/6 , m2 = 1kgpi m1 2 = 8m/s pi . pi :

() m1


2011-2012

() pi m1

() pi

()

(5+8+4+8 )

pi

pi

!!!

pi !


2011-2012

3 pi

:pi: : : 3

1 1.1 1.4 pi pi (4 5 = 20 )

1.1. - pi pi. pi pi :

() pi

() pi pi

() pi pi

() pi pi

1.2. pi pi pi 5pi6, t = 0 :

() A2

() A2

() A2

() A2

1.3 pi l, m pi pi f0. 3m, pi

() f03

() f0

()

3f0

()

3f03


2011-2012

1.4 pi - pi :

()

() pi

() pi2

() pi4

1.5 () pi () pi. (5 1 = 5 )

() pi pi .

() pi , pi .

() pi .

() S1 (k) - (m) S2 2k - (m) pi , S2 pi S1

() pi , pi

22.1 pi , pi . pi pi x = +A

2

pi :

() KU

= 13

() KU

= 1

() KU

= 3

pi pi pi .(3+4=7)


2011-2012

2.2. pi k, pi (pi ). . -pi m. pi . :

() 12m2g2

k.

() 12M2g2

k.

() 12

(m+M)2

kg2.

pi pi pi . (4+5 = 9)

2.3. pi , pi . pi pi d , pi . pipi , pi A(max)B(max)

() 12

() 1

() 2

pi pi pi. pi . (3+4 = 7 )

3

k = 900N/m, pi . pipi pi T = (pi/15)s. t = 0 pi pi = 6m/s pi . :

() pi .

() .


2011-2012

() pi pi pi pi 0 (2pi/15)s.

() pi pi K = 3U , pi K U .

(5+5+8+7 )

4

5

5

4

mN

100 = . 1 = 4 kg . 2 m = 1 kg 1 h, .

1 m20

d = , 2.

. h 1. 6

. .

6

. . 6

. .

7

g= 10 m/s2. . 102

k = 100N/m - pi. pi pi 1 M = 4kg pi pi. 2 m = 1kg pi pi pi 1 h, pi . 1 pi d = pi

20m

, 2.

() pi h - pi 1.

() pi - pi .

() pi pi .

() pi pi .

g = 10m/s2. pi2 10.

(7+7+6+5 )

pi

pi

!!!

pi !


2011-2012

1 - L C: : 75

minpi::

1 1.1 1.4 pi pi (4 6 = 24 )

1.1. pi LC pi- :

() pi pi

() pi pi

() pi pi

() pi pi pi

1.2. pi pi LC, pi pi pi pi :

()

()

()

()

1.3 pi L C pi pi - V0, I. pi pi pi 2V0, - :

() I

() I2

() 2I

() 4I


2011-2012

1.4 L C pi :

() pi

() pi pi pi pi .

() pi

22.1 L C (1) pi C pi pi L, L C (2) pi, pi pi 4L. pi (1) pi V pi (2) pi 2V .

(1) Q2Q1

:

() 1() 2() 1

2

pi pi pi .(5+4=9)

(2) E2E1

:

() 1() 2() 4

pi pi pi .(5+4=9)

2.2 pi q t L C.

I2I1

:

() 34

() 43

() 49


2011-2012

) 2.

) 4.

. .

( )

4.

q - t ,

0 t0, LC.

21

II

:

) 34

) 43

) 49

. .

( )

5.

C,

L , .

Q=100C ,

. t

q= 60C .

i=80mA. :

pi pi pi .(6+4=10)

3 L C pi pi C =

100F pi pi L. pi pi pi q = 104(100t)(S.I.).

() pi pi L pi

() pi

() pi t = 0

() pi pi pi pi q pi.

(10+12+12+14 )

pi

pi

!!!

pi !


2011-2012

2 - : : 75

minpi::

1 1.1 1.4 pi pi (4 7 = 28 )

1.1. LC , Q pi I pi :

() Q = LCI

() Q = LCI2

() I = QLC

() I = QLC

1.2. L C pi t = 0 pi 0, 4J . t = T + 3T

4 pi pi :

()

() 0, 1J

() 0, 3J

() 0, 4J

1.3 pi LC f . pi pi pi, f . pi f

f :

() 2

()

2

() 12

()

22


2011-2012

1.4 LC R. pi pi :

() pi

()

() pi

()

2

2.1 L C -, pi T . t0 pi pi pi .

t1 = t0 + T2 , :

() .

() .

() pi .

pi pi pi .(6+4=10)


2011-2012

6

3. LC 1 2 .

C1 Q1. T t0=0

1 , LC1 . 15T

t4

,

LC1, o 1 2. Q2 C2, C2=4C1, LC2

) Q1. )Q1/2. ) 2Q1.

4. (L1C1) (L2C2) .

(1) (2) C1 C2 , . 1/2 :

. 2. . 1

4. .

1

2.

5. (L, C) (L, C) . C.

. L, L

. L =4 L. . L =4 L. . L =2 L.

6. Q

q3

, q

Q ,

E

B

U

U

:

. 1

8 .

1

3 . 3

7. LC .

. . . . . .

8. LC. , . E/4 .

. /4 . 5/4 . 3/4 . 0

2.2 L C , pi C1 pi Q1.

t0 = 0 pi 1 , pi L C1 . t1 = 5T4 , pi pi L C1, pi 1 2. Q2 pi pi pi C2,piC2 = 4C1, L C2 :

() Q1

() Q12

() 2Q1

pi pi pi .(7+5=12)

3 pi pi E = 20volt r = 1 , R = 9 , pi C = 10F pi pi L = 16mH. pi (1) pi pi - . t = 0, pi pi (2) pi, pi L C .

() pi pi pi pi pi (1)

() pi pi pi pi pi pi pi pi pi pi pi pi pi


2011-2012

8

1.

=20 V

r=1 , R=9 ,

C=10 F L=16 mH. O

(1)

. t=0, (2)

, L-C

.

)

(1).

) ;

;

;

)

S.I. .

) .

) Ohm :

0 0E 20i A i 2A

R r 9 1= = =

+ +

:

2 3 230

B BLi 16 10 H (2A)U U 32 10 J2 2

= = =

() pi pi pi S.I. pi pi

() pi .

(12+12+12+14 )

pi

pi

!!!

pi !


2011-2012

1 - : : 3 pi::

1 1.1 1.4 pi pi (4 5 = 20 )

1.1. pi pi pi pi pi pi pi

x = 4 102(10t+ pi6

) (S.I.)

() pi 4 m.

() 40 102rad.() 4pi

6rad.

()

1.2. LC Q I. pi pi(VC(max)) :

() pi

() pipi

() pi

() pi

1.3 pi pi pi pi , pi pi f1,f2 pi pipi pi :

() pi -2 2 |f1 f2|.() pi 0 2 f1+f2

2.

http : //perifysikhs.wordpress.com .

2011-2012

() pi pi pi 0 2 f1f2

2.

() pi pi pi -2 2 f1+f2

2.

1.4 :

() pi pi b.

() pi pi b.

() pi pi pi .

() , pi .

1.5 () pi () pi. (5 1 = 5 )

() pi pi - pi.

() - pi - .

() pi pi pi pi pi pi , pi .

() .

() R L C pi pi.

22.1. pi pi - pi . pi pi pi .

. pi :

() 4s() 8s

http : //perifysikhs.wordpress.com .

2011-2012

2 2.1 (L1C1) (L2C2)

.

(1) (2)

C1 C

2 , .

1/2

:

. 2. . 1/4 . 1/2 . ( 1)

. ( 3)

2.2 , . .

. :

i) 4s ii) 8s iii) 16s

.

( 1+2=3)

. ;

i) 4

ii) 43

iii) 45

.

6

/2

4 2

(s)

() 16s

pi pi pi. pi . (1+2 = 3 )

. :

() pi4

() 3pi4

() 5pi4

pi pi pi.

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