# Find the period of the particle and the amplitude

1. May 14, 2010

### Maybe_Memorie

1. The problem statement, all variables and given/known data

A particle moves with SHM through two points p and q 1.2 metres apart. It takes 3 seconds to move from p to q and 3 seconds to move from q to q, i.e. passing q the next time.
Find the period of the particle and the amplitude.

2. Relevant equations
x = ACos(wt + a)
v = w(A^2-x^2)^1/2
a = -w^2x

3. The attempt at a solution
I drew a diagram, and tried associated circular motion, but the problem is I have no idea where to start the motion, or if I can take the point half way between p and q as being equilibrium.

2. May 14, 2010

### rl.bhat

Let O be the equilibrium position, and A and B are the extreme position. The particle takes 1.5 s to go from O to q and 1.5 s to go from q to B. So it takes 3 s to go from O to B. This interval is T/4. Hence T = 12 s.
If you measure the displacement from the equilibrium, then
x = Asin(2πt/T)
Here x = 0.6 m, T = 12 s and t = 1.5 s.
Now find A.

3. May 14, 2010

### ehild

Are the period and amplitude different if you start to measure the time later or sooner? You can take he phase constant equal to zero, a=0.

ehild

4. May 15, 2010

### Maybe_Memorie

It's never specified that it takes 1.5 seconds to go from O to q, just that it takes 3 seconds to gor from q to B to q. How did you come up with this?