EJSS Simple Harmonic Motion Velocity Model



From x = xo sin ? t
differentiating we get



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




Variation with time of velocity 
In terms of x:

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

v = x 0 ?( 1 ? ( x x 0 ) 2 )

v = ?( 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