### 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 ω t )
since

v = x0ω cos ωt

where x0 is the maximum displacement

v = ±x 0 ω( 1 − s i n 2 ω t )
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