. . : . . , . -1 2 3
( f )( ) . =
N f ! t
T. =
t T! N
.
1 f ! T 1 T! f
1
=
1
=
) . ( . :T T w.sin w.cos W
: .A
1 2 , .
= :( F )
m
F w
:(A ) .
3
: .
4
F
m
F
: .m
5
2A
F
F
. ( 2A )
T T F ! k .x
T T T T d k .x Fd x E T T m .a ! k . x T T kx T T @a aE x m
T T F ! Fd
F F
.F a
-x
+x
-x
+x
T d w . sin( U)
Ux si ( U) ! L
L
T
T x d mg . ! L
mg kp ! L
S T w.sin x W w.cos
T T Fd x E
:. . 2 . . = = 1
:( S.H.M ) . ( . ) 3
: .
T T aE x
.
Y
270 P 0 90 (U)
2
P y A
y sin U ! A
A : y = 90 o, 270 o ,
@ Y ! ASinU.y
:T 2T U
0
: = 0 o, 180 o , 360 o
v vx x
vy
co U !
v v
@ v ! v. cos U @ vy [.A. cos U
: .
(U) 2
. vmax = .A = 0 o,90 o, :
si
2
+ cos2sin(U) ! y A
= 1 cos2
=1- si
2
:
cosU ! s 1 sin2 U ! s 1
y A y !s 2 A2
2
2
2
:
T 3 vy ! v. cosUA2 y2 @ v y ! [.A. s A2
v y ! [. A 2 y 2
: v = - 10 Si ( 2 t ) : ,
,
([) v = - [ A Si ([ t ) v = - 10 Si ( 2 t ) [ t = 2 t [ = 2
rad\s :
1
v = - [ A Sin ([ t ) v = - 10 Sin ( 2 t ) [ A = 10 2A = 10 A! 10
! 5m 2
: :
2
: ( 0.1 ) s v = - 10 Sin ( 2 t ) = - 10 Sin ( 2 x 0.1 ) = - 1.98
m\s :vx ! [. s
3 4
(4)m
A 2 x 2 ! s 2 5 2 4 2 ! s 2 9 ! s 6m / s
: ax a x a ay
( ac )si ) a
( ay ) ay2
@ay
a. sin
.A. sin :
. 0 T 2T U amax = .2.A
= 90 o,270 o ,
:
a y ! [ .A. sin([t )
2
y ! A sin([t )a y ! [ .y2
:
(y
)
y ! ASinUvy ! [.A.CosUa y ! [ .A .SinU2
(1) ( 4 ) cm ( 10 ) cm\s : . =2.A 4 = 2.A A = 4 2 = 2 cm 1
(1). vmax= [ . A 10 = [ . 2 [ = 10 2 = 5 rad\s . [ = 2T \T2T 2 T
T! ! ! 1.25s [ 5
2
-3
(2). :y cm 3T 2 T 4
:
1
4
8
12
t 16 sec
-3 A = 3 cm
(2):x cm 3T 2 T 4
-2
4
8
12
t 16 sec
-3
T = t\n = 16 2 = 8 Sec
(2): -3
vmax= [ . A[! 2 2 ! ! 0.78ra \ s 8
vmax= [ . A = 0.78 3 = 2.35 cm\s
(2): -4
amax= [2 . A amax = ( 0.78 )2 3 = 1.82 cm\s2
