10 1 1

. (oscillatory motion) (periodic) 1 (period) (Simple Harmonic Motion, SHM)

T

10-1 SHM

2

2

2

d xF ma mdt

= =KK K (1)

F kx= K K (2) (1) = (2)

2

2

d xm kdt

x=

2

2

d x k xdt m

=

2

2 0d x k xdt m

+ =

2 km

=

2

22 0

d x xdt

+ = SHM SHM

10 - 2

( ) sin( )x t A t = + ( t ) + (Phase) t = 0 (angular frequency) A (Amplitude)

SHM

[ sin( )]dx dv A tdt dt

= = + cos( ) ( )dv A t t

dt = + +

cos( )v A t = +

2 2 2 2cos ( )v A t = + 2 2 2 2[1 sin ( )]v A t = + 2 2 2 2 2[ sin (v A A t )] = + 2 2 2 2( )v A= x

2 2v A= x

2

2

d x dvadt dt

= =

[ cos( )da A tdt

] = + 2 sin( )a A t = +

2a x=

2 2v A= x

( ) 0x = v 2 0v A=

maxv A=

2a x= ( x A= ) a 2maxa A=

10 - 3

10-2

( ) sin( )x t A t = +

10-3 SHM SHM SHM

2 2 21 1 ( )2 2k

2E mv m A x= = ( 0x = ) x A= x A= = 0

2 21 12 2p

2E kx m x= =

10 - 4

0x = x A=

2 2max

12p

E m A=

k pE E E= + 2 21 1

2 2E mv kx= +

2 2 2 21 1( )2 2

E m A x kx= + 2 2 2 2 2 21 1 1

2 2 2E m A m x m x = +

2 212

E m A=

212

E kA=

x

10 - 5

10-4 SHM F ma =

2

2

d xkx mdt

=

2

2 0d x k xdt m

+ = SHM

2 km

=

2

22 0

d x xdt

+ =

km

= 2 f = 2 kf

m =

SHM

12

kfm=

SHM

2 mTk

=

10 - 6

10-5 SHM sinF mg = SHM 5o sin F mg= F ma = mg ma = 0ma mg+ =

2

2 0d S gdt

+ =

2

2 0d L gdt + =

2

2 0dL gdt + =

2

2 0d gdt L + =

SHM

2

22 0

ddt + =

gL

= 2 f = 2 gf

L =

SHM

12

gfL=

SHM

2 LTg

= ( L )

10 - 7

10-6 SHM ( )( )sinmg d =

2

2

dI Idt = =

2

2 sindI mgddt =

2

2 sin 0dI mgddt + =

sin

2

2 0dI mgddt + =

2

2 0d mgddt I + =

SHM

2

22 0

ddt + =

mgdI

= 2 f = 2 mgdf

I =

SHM

12

mgdfI=

SHM

2 ITmgd

=

10 - 8

10-7 SHM () SHM = (kappa) I = I =

2

2

dIdt =

2

2 0ddt I + =

SHM

2

22 0

ddt + =

I =

2 f = 2 f

I =

SHM

12

fI

=

SHM

2 IT =

10 - 9

10-8 SHM ()

O

R

x

y

O B

A

B

xK

yK

cosx R = cosx A t= cos( )x A t = + siny R = siny A t= sin( )y A t = +

10 - 10

10-9 (Damped oscillation)

2E A A (damped oscillation)

- -

F kx bv=

b

bv

F ma = kx bv ma = 0ma bv kx+ + =

2

2 0d x dxm b kxdt dt

+ + =

2

2 cosb tmx Ae t

= 2

24k bm m

= 0 =

10 - 11

2

2 04k bm m = 4b k= m

4b k= m 4b k> m overdamp 4b k< m underdamp

10-9 (Forced oscillation)

(resonance)

10 - 12

10-1 4 N 0.02 m 2 kg 0.04 m . . 2 kg . . . .

10 - 13

10-2 SHM 10-1 = 0.05 m 2 ms-1

10 - 14

10-3 5 kg 0.1 m 0.05 m SHM 10-4 10-8 10-5