A simple harmonic motion question?

Question

A particle oscillates with a mass of (10)g and an amplitude of (2)mm. If it's maximum acceleration is (8X10^-3)m/s^2 write the function of the forces that influencing it as a function of time.

note: sorry about my crappy language as it's my first time writing aproblem in english ><

Answer 1

For a simple harmonic motion
a=dv/dt=-M sin(wt+pi/2)=8 E-3 m/s^2
(Phase angle pi/2 since a has a max value at this point)
w=2pif
f= 2pisqrt(k/m)
k=? lets not despair yet.
We know that
Amplitude=M/w^2= 2mm=.002m
then
M =.002/w^2
Also M= 8 E-3
w= sqrt(.002/(8E-3))=0.5rad /sec

Finally we have
F=ma
F(t)= m (8E-3)sin(0.5t + pi/2)
F(t)= .08 sin(0.5t + pi/2)