Example

The graphs show how the variation with time of the velocity, v and the acceleration, a of a body when it is oscillating with simple harmonic motion. 
(a)    Determine the period, T.
(b)    Sketch the variation with time of the displacement, x, of the oscillating body
[ 2.09 s, x = 2  sin( 3t )]

Solution:

a) maximum velocity , v0 = x0ω = 6 m/s

maximum acceleration a0 = x0ω2 = 18 m/s2

thus dividing the 2 equations, we get ω = 3 rad/s

therefore since ω = 2 π T

3 = 2 π T 

T = 2 π 3 

T = 2.09 s 

b) since maximum velocity , v0 = x0ω = 6 m/s and we now know ω = 3 rad/s earlier

x0(3) = 6

x0 = 2 m

using the model to test check out your answer!


Model:

http://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHM11/SHM11_Simulation.xhtml