SHM Chapter 16 v,a vs x practice 1

Example

The graph of velocity against displacement of a body is shown below.

a)     Explain why there are two values of velocity for zero displacement.
b)    Explain why there are two values of displacement for zero velocity.
c)    Using the maximum value of the velocity, determine the period of oscillation.
[when x =0, v =8(moving right) or -8(moving left),when v =0 , x = -2(at left) or 2(at right),1.6]

Hint:

http://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHM16/SHM16_Simulation.xhtml

Suggested Solution:

a)    An oscillating body moves through the equilibrium position (zero displacement) alternately in opposite directions.

b)    An oscillating body has zero velocity when its displacement is maximum which occurs at the  maximum amplitude positions. Hence, there are 2 values of displacement.

c)    v_o = xo ω      
   
(8.0) = (2.0) ω
ω = 4.0 rad/s        
thus 
  $$T=\frac{2\pi }{\omega }$$  T  = 1.57 s = 1.6 s   (to 2 s.f.)

Model:

http://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHM16/SHM16_Simulation.xhtml