7. J 2012/2013.

j , j j

18-19. 5. 2013.

1: (10 )

j j j 19. j. j j j . (). j , j j j . j .

j m = 57 g, j a oj j D ( 1)j I = 0,057 kg m2. j, j j j .

o

D

31 cm 36 cm

d

1:

() j jj . D, j o. o , j . j j d D ( 1). v , d, I m. j j j j , j j j. j, j j . (1,5 )

() - j . j j j d D (1). D, j o. j j e j . e j I, m

1: 1 3

7. J 2012/2013.

j , j j

18-19. 5. 2013.

d. j j j j , j j j. j, j j . (1,5 )

j ( 2), . j . J- , , . j j S j. j .

2: - 3:

() , ( ) . . j j j j F = RN , j R j , N j -. j j j , N a ( 3). j 3, F j , j jF R, j R . a j R, R, m M . j a j R = 32,5 mm, R = 0,05,m = 57 g M = 180 g. j j j IL =

2

3mR2. (2 )

1: 2 3

7. J 2012/2013.

j , j j

18-19. 5. 2013.

() j , j - j j . j j j j j j e =

v2yV2yv1y

, v1y v2y j y -

, V2y j y ( S). j 2. j j eP =

v2yv1y

. eP j e,

m M . j eP j e = 0,9, M m j j (). (1 )

() 1 = 450 v1 = 30

m

s(

S, 2). j 1 = 300rad

s

j 2. N j j j (). 2 j S . j 2 S. j m,M , R, R, eP a . () (), eP = 0,40 a = 3,0 mm. j S , ? (4 )

: , ,

: J, ; , ,

j : , ,

1: 3 3

7. J 2012/2013.

j , j j

18-19. 5. 2013.

2: (10 ) a j j - j - . j , , j. j - j 1880. , , , , (, ).

1:

j -j j j j - . J jj j j (1), j je a - j, , , , - j.

A: - (4 )

j . -, S m, - j (2). j - , j n . j k. j - , j j X0.

2: J

.1. U . , j - j X1. Fq U X0, X1, S, k n.

.2. , j j x j, U . x X0, X1, k,n, m x, j j 0 X0, X1, k, n m.

.3. j L -. j j j X1, j j j x. j j j x q . x q X1, S, k, n, m, L, U , x q.

2: 1 3

7. J 2012/2013.

j , j j

18-19. 5. 2013.

.4. j j, x = 2x q = 2q. -j X0, X1, S, k, n, m L. j j j j X0 X1 j ?

: (1,5 )

- j - . e j - , - j j j b = 7,83 106 kg/s. j , j j (a 3). j j , j , - . j -j . j j j j .

3: K

, -, j. x j j j j - j j j ( j j x). j j- :

x+ x+ 20x = f0 cos(t+ ).

j . e j m = 0,243qV , je - q = 2659 kg/m

3, V j j . -

j j k = EWD3

4L3, j J E =

7,87 1010 N/m2, W = 0,127mm, D = 0,325mm L = 2,809mm j .

.1. a j j - m, k, x, b F = F0 cos(t+ ).

.2. j 0.

.3. j e x = x0 cos(t + ). x0 j = f0, , 0.

2: 2 3

7. J 2012/2013.

j , j j

18-19. 5. 2013.

: (3 )

q j j j x, j - = 8,13 106 C/m. j , j. q j x, j j - Re, j Le Ce.

.1. j , - j j e.

.2. j .

.3. Re, Le Ce - j .

.4. e - , - . j .

: j (1,5 )

E j j - . 4 j , j a je f = 215 Hz.

.1. jj - j ?

.2. j - - ?

.3. j j -.

.4. jj , j - j jj 25 oC, -j jj 10 oC?

4: j

: , ,

: , ,

j : , ,

2: 3 3

7. 2012/2013.

18-19.5.2013. ,

3: (10 )

, , 31,1mV = . 0 0,187kgm = .

o1 20 Ct = 5

0 1,013 10 Pap = . 31 1,2kg/m= .

) 2t ? (2) ) o3 110 Ct = .

. . (2) ) ( ). o3 110 Ct =

o20 C 50 1,013 10 Pap = . h ? (2) ) h ( ) 10mh = . . (4) 29,81m/sg = .

* * * * * * * * * *

0

0

0( ) gx

px e

= , 0 0p 0x = . axe , a 1ax : 1axe ax .

: , , : . , , : , ,

7. J 2012/2013.

j , j j

18-19. 5. 2013.

1:

() j 12I2 = 1

2mv2 + 1

2I21, j 1

. jj o D I = mvd+ I1. j v =

2IdI+md2

.

j d =

Im

= 1 m. j d = 1 m j , j. d = 67 cm. j , j. d = 31 cm.

() j 12mv2 = 1

2mv21 +

12I2, j v1

. jj o - D mvd = I mv1d. j j j e =

v1v.

j e = Imd2

I+md2. j e(d)

d 0 d =

Im

= 1 m. j ,

j (d = 67 cm), j (d = 31 cm).

() j jmdvxdt

= F M dVxdt

= F ,

a j ILddt

= FRNa. j vx R =

Vx, j.dvxdt Rd

dt= dVx

dt. j F = RN . j

a = RR(

53

+ 2m3M

)= 3,05 mm.

() y mv1y = MV2y +mv2y. -j e eP eP =

eMmM+m

= 0,443.

() S j: 1) j ; 2) , . j j IL

ddt

= FR

mdvydt

= N , j t1 -

t2 j m (v2y v1y) = t2t1Ndt IL (2 1) = R

t2t1Fdt,

2 t2. v2y = eP v1y F = SN , j j- j 2 = 1

3v1 sin 12R

S (1 + eP ). j -

j m (v0x v1x) = t0t1Fdt, IL (0 1) =

t0t1FRdt

MV0x = t0t1Fdt, j t0 j , -

0 j . v0x + R0 = V0x j

t0t1Fdt = v1 cos 1+R11

M+ 5

2m

, j

0 < 0. j ( j F j () j 0 < 0) jj j IL (2 1) =

t0t1FRdt

t2t0FRdt+

t2t0Nadt

m (v2y v1y) = t0t1Ndt+

t2t0Ndt. j

j j F = SN , j F = RN , j

7. J 2012/2013.

j , j j

18-19. 5. 2013.

2 = 11+

v1 cos 1R

5

3+ 2m

3M

(1 + eP )v1 sin 1

R32

(R

aR

)+ 1

S

(R

aR

)1+

v1 cos 1R

5

3+ 2m

3M

. j-

2 j 1) 2) j j

grS =

v1 cos 1+R1(1+eP )v1 sin 1(mM +

5

2)

= 0,359, S < grS

, S > grS . -

j 2 S j . S = grS

j j .

0 0.2 0.4 0.6 0.8S

-300

-200

-100

0

100

200

300

2[rad/s]

1: 2 S

7. J 2012/2013.

j , j j

18-19. 5. 2013.

2:

A: -

A.1. (0,5 ) j j j , mg = nk(X X0), j X . , j - j mg + Fq = nk(X X1), j Fq = nk(X0X1). j - j q0 =

0SX1U . j Ep j j .

j, , 2SEp =q00. j j

j j Fq = q0Ep =q20

20S= 0SU

2

2X21

= nk(X0X1), j

U = X1

2nk(X0X1)

0S.

A.2. (0,5 ) j X1 + x , -

j j j F q =0SU2

2(X1+x)2

0SU2

2X21

0SU2

X31

x = Fq 0SU2

X31

x,

j F e = nk(X X1x). mx = F e mg F

q (nk

0SU2

X31

)x = nk(3 2X0X1)x. , j

j j 0 =

nkm(3 2X0

X1). j

j 3X1 > 2X0.

A.3. (2 ) U = Lq + (q0+q)(X1+x)0S

, j

q0 =0SUX1

.

j qx, j q = ULX1

x X1L0S

q.

j Fq =q20

20S. j F q =

(q0+q)2

20S

q20

20S+ q0

0Sq, j F e = nk(XX1x).

x = nkmx U

mX1q.

A.4. (1 ) j x = 2x q = 2q j .3. j: (2 X1

L0S)q U

LX1x = 0 (2 nk

m)x U

mX1q = 0. j

j j (2 X1L0S

)(2 nkm) = U

2

mLX21

= 2nk(X0X1)mL0S

.

21 =nkm 22 =

X1L0S

, j jj:

4 2(21 + 22) +

21

22(3 2X0/X1) = 0. j

= 12

[21 +

22

41 +

42 2

21

22(5 4X0/X1)

]1/2,

j j, j 3X1 > 2X0.

:

.1. (0,2 ) J j jmx+bx+kx = F0 cos(t+).

.2. (0,3 ) j j .1. m j j - j j , j -

j = bm= b

0,243 qWLD= 104 s1 0 =

km=

ED2

0,972 qL4= 2,27 105 rad

s.

7. J 2012/2013.

j , j j

18-19. 5. 2013.

.3. (1 ) x = x0 cos(t+) j x+x+20x = f0 cos(t+ ),

j = f0 = F0/m, j 2x0 cos(t + ) x0 sin(t + ) +

20x0 cos(t+ ) = f0 cos(t+ ) cos + f0 sin(t+ ) sin . j sin(t + ) cos(t + ) j j x0(

2 20) = f0 cos

x0 = f0 sin , j x0 =f0

(220)2+22

= arctg 22

0

.

:

.1. (1 ) j j j P = xV0. j j , P = 2F0x. jV0 = 2F0.

.2. (0,6 ) j , j j m

q + b

q + k

q = F0 cos(t + ) =

2V0 cos(t+ ).

.3. (0,7 ) j Leq + Req + q/Ce = V0 cos(t + ),

j Le =2m2

= 2,27 kH, Re =2b2

= 237 k, Ce =2

2k= 8,54 fF.

.4. (0,7 ) j ReLeCe j - C j . j 1.

1:

: j

.1. (0,1 ) j j ff

= 0, t0 = 25

C.

.2. (0,1 ) j ff

= TT

< 0, .

.3. (0,8 ) j j , j t0 = 25

C , j ff

= (t t0)2, j j

j . j , . (70 106,10 C),j = 7010

6

2025 C2= 3,5 108 C2. , j -

j f(t) = (1 3,5 108(t/C 25)2) 215Hz.

.4. (0,5 ) , - T . f

f= T

T T = f

fT = 3,5 108(10 25)2

365 24 60min 4,14min, .

7. 2012/2013.

18-19.5.2013. ,

3: ) : 2 0 1 Vg m g Vg+ = (0,5), 2 2t . : 0 1 2( )m V= (0,2). 1T 2T , : 1 1 /p RT M= (0,5) 2 2 /p RT M= (0,5). : 12

0

1

1

TTm

V

=

(0,2). 2 341KT =

o2 68 Ct = (0,1).

) 3 383KT = , 3 0gF Vg m g= + (0,5). : [ ]1 1 3 0( )T gF Vg F V m g = = (0,3). ) : 1 3 3 1 / /T T= (0,6), : 11 0

3

(1 )TTF V m gT

=

(0,5). 1,2NTF = (0,1).

) h : 3 0 hVg Vg m g= + (0,7) : 3 0 /h m V= + (0,3).

h : 1

0

1

gxp

h e

= (0,4).

h : 0 01 111 1

0 13

ln ln 843m

h

p p Vh Tg gm V

T

= =

+ (0,6).

) h h+ : 1 1

0 0

( )

1

g h h g hp p

h h he e

+

+ = = (1). , 31

0

10 1

g hp

, 1

0

(1 )h h h

g hp+

(0,5). : 2

10 3 0 3

0

( ) ( ) hh h

gm V a m V g Vg V h k h

p++ = + + = (1,5).

:

0 3 0 3 0 02

h 1 1

( ) 22 2 186s

m V m V p pTk g V g+ +

= = = = (1).

7. 2012/2013.

- 1 4

18-19. 5. 2013.

,

(20 ):

(LEDLight Emitting Diode) . , LED , .

LED. (photodiodePD). , ( , W/m2).

: 1) PD . 2) LED . 3) LED, . LED.

. , LED p-n . LED, p-n , :

: - - -

LED ( ), LED.

LED :

LED LED ( LED). LED .

. . e, a , . .

( ) ( )

.

7. 2012/2013.

- 2 4

:

1. ,

2. , 3. , 4. , 5.

LED ,

6. ,

7. , . , DCV V , ( ).

a , X Y . LED X , Y ( 1). . 2. LED . LED .

1. .

2. .

7. 2012/2013.

- 3 4

: LED .

:

(1) LED , . LED.

(2) ( Y-) LED. LED

. LED . . .

(3) LED , . LED.

(4) .

1. (5 )

1.1 LED ( ). LED . LED LED X-, .

( ) . , LED . 10 . . (2 )

1.2 1.1 . (3 )

2. LED (5 )

2.1 ( ) LED.

LED . . ( ) . LED . LED . LED .

LED . 20 0-2 V 5 2-6 V . . (3 )

2.2 LED LED . . (2 )

7. 2012/2013.

- 4 4

3. LED (10 )

3.1 ( ) y- , LED

. LED. LED , .

. ( ) . . (3 )

3.2 3.1. (

/ ) LED . (7 )

:

. . LED . . . . R1 ( 100 k).

. .

: , , : , , , , : , ,

7. 2012/2013.

- 1 6

18-19. 5. 2013.

,

1.1 LED

( ) .

(

) ( ) LED :

(1)

x (mm)

(mV) (mV) (A)

-1/2 (A

-1/2)

0 981 113 8,68 339

30 591 180 4,11 493

60 446 215 2,31 658

90 379 220 1,59 793

120 325 240 0,85 1085

150 309 243 0,66 1231

180 304 250 0,54 1361

210 286 244 0,42 1543

240 276 240 0,36 1667

270 266 237 0,29 1857

300 260 236 0,24 2041

1.2 LED . ,

LED LED

:

( )

(2)

x , d , LED . LED:

( )

(3)

:

(4)

-1/2

x, , .

7. 2012/2013.

- 2 6

0 50 100 150 200 250 300

500

1000

1500

2000I P

D (A

-1/2

)

x (mm)

2.1 LED

( ) . R3 (

) (

) LED :

(5)

(mV) (V)

(mV)

(mV) (mA) (mW) ( A)

/ (mA/W)

23 1,662 148 144 0,0767 0,127 0,04 0,3139

100 1,711 176 153 0,333 0,570 0,23 0,4033

151 1,725 179 143 0,503 0,868 0,36 0,4146

201 1,735 202 153 0,67 1,16 0,49 0,4215

254 1,744 223 159 0,847 1,48 0,64 0,4334

313 1,751 240 160 1,04 1,83 0,8 0,4379

408 1,762 270 162 1,36 2,4 1,08 0,4507

517 1,771 303 165 1,72 3,05 1,38 0,4522

603 1,777 334 171 2,01 3,57 1,63 0,4564

709 1,784 372 177 2,36 4,22 1,95 0,4625

807 1,79 398 176 2,69 4,82 2,22 0,4610

915 1,796 433 179 3,05 5,48 2,54 0,4639

1023 1,802 468 180 3,41 6,14 2,88 0,4687

1116 1,806 492 179 3,72 6,72 3,13 0,4659

1196 1,809 518 183 3,99 7,21 3,35 0,4645

1322 1,815 552 180 4,41 8,0 3,72 0,4651

1425 1,819 583 181 4,75 8,64 4,02 0,4653

7. 2012/2013.

- 3 6

1526 1,822 614 179 5,09 9,27 4,35 0,4694

1632 1,827 646 182 5,44 9,94 4,64 0,4669

1693 1,828 668 184 5,64 10,32 4,84 0,4692

1807 1,832 698 180 6,02 11,03 5,18 0,4694

1904 1,835 733 187 6,35 11,65 5,46 0,4688

1990 1,838 765 192 6,63 12,19 5,73 0,4699

2660 1,857 962 190 8,87 16,47 7,72 0,4689

3010 1,866 1063 187 10,03 18,72 8,76 0,4679

3430 1,876 1179 179 11,43 21,45 10,0 0,4662

4160 1,892 1401 182 13,87 26,24 12,19 0,4646

4580 1,9 1518 177 15,27 29,01 13,41 0,4623

5220 1,911 1694 177 17,4 33,25 15,17 0,4562

5840 1,922 1876 178 19,47 37,41 16,98 0,4538

6270 1,93 1996 176 20,9 40,34 18,2 0,4512

2.2 LED . :

(6)

. LED

(7)

(8)

LED

LED 5 mA.

7. 2012/2013.

- 4 6

0 5 10 15 20

0.30

0.35

0.40

0.45

I PD/P

LED

(mA/W

)

ILED

(mA)

3.1 LED, ILED LED

, . ( ) ri , . , . LED .

R3 (

) ( ) LED

( ):

(9)

(mm) ( ) (mV)

( ) (mV) ( ) ( A)

( ) ( Am)

0 561 140 4,21 0

1 522 136 3,86 3,86

2 476 133 3,43 6,86

3 443 127 3,16 9,48

4 394 119 2,75 11,0

5 333 115 2,18 10,9

6 279 111 1,68 10,08

7 234 99 1,35 9,45

8 206 93 1,13 9,04

9 186 88 0,98 8,82

10 159 83 0,76 7,6

7. 2012/2013.

- 5 6

11 131 79 0,52 5,72

12 109 75 0,34 4,08

13 100 72 0,28 3,64

14 89 68 0,21 2,94

15 83 66 0,17 2,55

16 79 65 0,14 2,24

17 74 61 0,13 2,21

18 71 59 0,12 2,16

19 68 57 0,11 2,09

20 67 57 0,10 2,00

21 66 57 0,09 1,89

0 5 10 15 20

0

1

2

3

4

I PD (A)

ri(mm)

3.2 , LED . a .

7. 2012/2013.

- 6 6

LED . ( , ). i- . , , LED, :

( ) ( ) ( ) (10)

je ( ) , ( ) , q .

:

( ) ( ) (11)

:

( ) ( )

(12)

o , i- :

( ) ( )

(13)

LED je:

( ) =

( )

(14)

( )

(15)

LED

(16)

LED. LED, , . (15), LED je

( ) . (16) .