# Find the period of the particle and the amplitude

## Homework Statement

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.

## Homework Equations

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

## 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.

rl.bhat
Homework Helper
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.

ehild
Homework Helper
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

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.

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?