Hi, I'm not very good at my mechanics, notably simple harmonic motion. I have been given this question:
A particle P moves with simple harmonic motion and comes to rest at two points A and B which are 0.24m apart on a horizontal line. The time for P to travel from A to B is 1.5s.
The midpoint of AB is O. At time t = 0, P is moving through O, towards A, with speed u m/s
a) Find the value of u
b) Find the distance of P from B when t = 2s
c) Find the speed of P with t = 2s
a) I know T = 2pi/w, as it takes 1.5s to go from A to B, that means T=3
Therefore w = 2pi/3
I know v² = w²(a²-x²)
but I don't know how that helps?
Am I doing it right so far?
EDIT: We are told that at t = 0 x is effectively 0, so:
and v = u
so u =(2pi/3)a
But what's next? How do I find a?