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 Author Topic: EJSS Simple Harmonic Motion Velocity Model  (Read 1234 times) 0 Members and 1 Guest are viewing this topic. Click to toggle author information(expand message area).
lookang
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 « Embed this message on: February 15, 2015, 01:33:11 pm » posted from:New York,New York,United States

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
 SHMvvsx.gif (264.31 KB, 640x304 - viewed 302 times.) *** There are 2 more attached files. You need to login to acces it! Logged
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