PHYSICS 5B Lecture Notes - Lecture 13: Angular Frequency
General function for simple harmonic motion :X =Acos (wt +8)
T= 2¥
,F=÷
v=E¥ '
- -WAS in (wt +f) =Vmax
a=E¥= -w2A cos (wt t8)=-wx
e± :Abody
oscillate
with simple harmonic
motion along The x-axis .Its displacement varies with Time
according to The equation :X=4cos (It +¥)where tis in seconds and The angle in then
parenthesis are In radius .
(a) Determine the amplitude ,
freguend and period of The motion
(b) Calculate the velocity and acceleration of The body at any time TH
(c) Using the results of (b) ,
determine the position ,velocity ,
and The acceleration of the body at t=
Is
(d) Determine The maximum speed and the maximum acceleration of the body
(e) Find the displacement of the body between to and t=
Is
HI What Is The phase of the motion at
t=2s
(a) A =4 ,T= 2¥ =2s
,
f =+2=0.5 (Hy
(b) V= 9¥ =.4sin (wt +f) ×(w)
=-4W sin (wt +8) .
=-4IT sin (at +¥)
a=E¥t =-4#cost ,t +¥).(a)
(C) X=4cos (a+¥)
=4cos (59/4) =4/-0.707 )
=-
2.83mV
=
-4h sin (5¥ ).
' -471 (-0.707 )
=8.89 (Mls )
a=.4t4os( 5¥)=27.9 mlsz
(d) Max speed
v. -
±4T ,(mls)
a=±4#
2(mlsz)
(e) t=O xo =4cos (o+±4 )=2.83 m
t =1×
,
=-2. 83 m
ox =×
,
-Xo =-2. 83 m
-2.83 m=-5.66 m
(f) 0= ?
t =2S
0=wttf = a×2+¥=(9¥)rad
in degree ⇒9.4=405 degrees
Irad =573 degree
spring .Mass System ← x=o→
fkuiiymatre
"Equuuefmf
F- ×
x =0
recall a=.w2×
spring constant (stiffness at the spring)
F= Ma =-mw2×
Document Summary
= e = - w2a cos ( wt t 8 ) wx with simple harmonicmotion along. A body according to parenthesis are (a) (b) Th (c) using the results of (b) determine the position , velocity , and. The acceleration of the body at t= (d) determine. The maximum speed and the maximum acceleration of the body (e) find the displacement of the body and t= to. = +2=0. 5 ( hy f at (a) (b) 4 # cost , t (a) (c) 2 ( mlsz) (e) t=o xo = 4 cos ( o. 2 + = (9 ) rad in degree. Equuuefmf recall a = w2 spring constant stiffness at the spring) A restoring force that is proportional to the displacement but opposite in sign. Is attached to a spring whose spring constant. The block is pulled a distance xtll am from. Its equilibrium position at x=0 on a frictionless.
