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SHM09

1.2.3 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

1.2.3.1 Model:

  1. Run Sim
  2. http://iwant2study.org/ospsg/index.php/72
 

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Parent Category: 02 Newtonian Mechanics
Category: 09 Oscillations
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