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Easy Java Simulations (2001- ) => Collaborative Community of EJS => Topic started by: lookang on February 15, 2015, 01:33:11 pm



Title: EJSS Simple Harmonic Motion Velocity Model
Post by: lookang on February 15, 2015, 01:33:11 pm
EJSS Simple Harmonic Motion Velocity Model

[lookangframe name=SHM09]

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