physics about harmonic motion

acceleration of s.h.m. = -w^2Acos(wt+phi) ,
w= angular speed, A=amplitude, phi= initial phase
max. accel. = 4pi (ms^-2) when cos(wt+phi) = -1
Hence, w^2A = 4pi
Velocity of s.h.m = -wAsin(wt+phi)
When sin(wt+phi) = -1, velocity = wA = max. = 8 (ms^-1)
Solving,
w = 1.57(s^-1)
Period T = 2pi / w = 4(s)//
A = 5.092958179 (m)//

The following two formulae are relevant:
a = w^2.x
v = w.[square-root(A^2 - x^2)]
where a is the acceleration of the oscillating object
w is the angular frequency of oscillation
v is the velocity of the object
A is the amplitude of oscillation
x is the displacement.

For max acceleration, a(max) = w^2.A
i.e. 4.pi = w^2.A
For max speed, v(max) = w.A (because max speed occurs at x = 0 m)
i.e. 8 = w.A
Dividing, 4.pi/8 = w
i.e. w = pi/2

But w = 2.pi/T, where T is the period of oscillation,
hence, 2.pi/T = pi/2
T = 4 s

A = 8/w = 8/(pi/2) m = 16/pi m = 5.09 m