Velocity LO (f)

From x = xo sin ω t 

differentiating we get

v = d x d t = x 0 ω ( s i n ω t ) = v 0 c o s ( ω t )

where   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 ωt )
      
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

Model:

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