# Oscillary Motion

1. Nov 11, 2004

The Problem is:
A particle executes simple harmonic motion with an amplitude of 2.25 cm. At what position does its speed equal half its maximum speed?

I've been looking at this for a while, and I cant see how to solve it without more information.

If I knew the energy and mass I could solve it,
if I knew the frequency or period I could solve it,
if I knew the spring constant and mass I could solve it,
but I dont have any of this, what's the trick?

2. Nov 11, 2004

### Tide

HINT: For what value of z does cos z equal half its maximum value?

3. Nov 11, 2004

### ehild

The position of the particle x=Asin(wt), A= 2.25 cm.
The velocity of the particle v= Awcos(wt).
The maximum velocity is Aw.
You look for the position when v=0.5 Aw.
0.5 Aw = Aw cos(wt) ----> cos(wt)=0.5.

You only ned to find sin(wt) to get x.

ehild

4. Nov 12, 2004

### CartoonKid

You can apply the general velocity formula for SHM here. since maximum velocity is v=rw, then take the half of it and equal to general formula. Work it out and you should be able to find the positions.