# SHM Equations of Motion

1. Jun 18, 2011

### ProPM

Hi

I am a bit lost with the equations for velocity:

I don't know Calculus yet, so my teacher just gave me the equation:

-wx0cos(wt) (w being omega)

He then said: v0 = wx0

and therefore, concluded: -v0cos(wt)

and then for when the displacement is maximum at time = 0: v0cos(wt)

Is this correct? I mean, I am obviously not doubting him but I am a bit confused plus my notes were not very organized on this day...

2. Jun 18, 2011

### rl.bhat

when t =0, ωt = 0 and cos(ωt) = 1

So vo = -xo*ω

3. Jun 18, 2011

### ProPM

So the equation would be:

v0cos(wt)

and for sin, how would it work?

Last edited: Jun 18, 2011
4. Jun 18, 2011

### mukundpa

The sign and the function sin or cos depends on the instant you are taking t=0. If t is taken zero when the particle is at the equilibrium position (x=0) than the equation for displacement will be x= A sin wt and that for velocity will be v = Aw cos wt

thus at extreme position wt = 90 deg, gives x = A and v = 0.
(A is amplitude and Aw = Vo, the maximum velocity)