1. Simple Harmonic Motion

A particle is moving with SHM of period pi seconds and maximum velocity 8 m/s. If the particle started from rest at x=a, find a, then find the velocity when the particle is distant 3 m from the mean position.

So i did...

Let motion be x =acosnt
period = 2pi/n = pi
hence, n = 2
x = acos 2t ---------(1)
v = -2a sin 2t
For maximum velocity, sin 2t = -1.
8 = -2a * -1
a =4

Am I right so far???

I have no idea how to find the velocity . I thought i would let x = 3 and sub into one but I didnt get the answer provided.

2. Use the relation

$v^2 = n^2( a^2 - x^2)$