EJSS Simple Harmonic Motion Velocity Model

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EJSS Simple Harmonic Motion Velocity Model



From x = xo sin ω t
differentiating we get



v = d x d t = x 0 ω  s i n  ωt  = v
0 cos ω twhere  v0 = x0 ω  is the maximum velocity




Variation with time of velocity 
In terms of x:

 
From mathematical identity  cos2 ωt + sin2 ωt = 1,
rearranging
cos2 ωt  = 1 - sin2 ωt
c o s ω t = ±( 1 − s i n 2 ω
  t )
 
since
v  =  x0ω cos ωt
where x0 is the maximum displacement
v = ±x 0 ω( 1 − s i n 2 ωt )
 
 
v = ±x 0 ω( 1 − ( x x 0 ) 2 )

v = ±ω( x 0 2 − x 2 )


 
 
Variation with displacement of velocity


http://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHM09/SHM09_Simulation.xhtml


Model:


http://dl.dropboxusercontent.com/u/44365627/lookangEJSworkspace/export/ejss_model_SHM09/SHM09_Simulation.xhtml