Harmonic Oscillator Acceleration! Help!?

Question

Using the fact that acceleration is the second derivative of position, find the acceleration of the block as a function of time.

Express your answer in terms of w, t, and x(t).

I'm having troubles with many of these types of problems....can anyone help?

Answer 1

Since you did not specify the starting point I assume a harmonic oscillator with
x(t)=A cos(wt)
v=dx/dt=-Aw sin(wt)
a=dv/dt=-Aw^2 cos (wt) substitute Acos(wt)=x(t)
a=-w^2 x(t)