Tuesday, January 13, 2015

SHM Chapter 09 v with x

Velocity LO (f)

From x = xo sin ω t
differentiating we get



v = d x d t = x 0 ω  s i ωt  = v0 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