Harmonic Oscillation Problem?

Question

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

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

**Note: the general solution for the position of a harmonic oscillator is given by the equation:

x(t) = C cos(omega*t) + S sin(omega*t)

where C, S, and omega are constants.

**I found the acceleration in the previous part of this problem in terms of setting F = -kx and F = ma equal to each to be:

a(t) = -(k*x(t)) / m)

Answer 1

x(t) = C cos(w*t) + S sin(w*t)

at t=0, x = xo,

xo = C *1 + S* 0

C = xo >>>>>>>>>>>

-----------------------

v = velocity = dx/dt = w[C sin wt - S cos wt]

at t=0, v=0 (released from rest)

0 = w[C*0 - S*1] = - w S

S =0 >>>>>>>>>>>

w^2 = k/m >>>>>> from your equation

a = -w^2 x = -kx/m

x = xo cos wt = xo cos [root{k/m} *t]