chap10 oscillation
DESCRIPTION
OscillationTRANSCRIPT
-
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