Classical Mechanics - Special Interest Problem

Consider a sinusoidal time varying force given by

Assume one dimensional motion such that the equation of motion is given by

m = F(t) = Asinwt

1. Find the general expression for x(t) in which the initial position is x_o and the initial velocity is _o.
2. Sketch x vs t over a few cycles of the periodic force.
3. What initial conditions are necessary for the motion to be bounded? That is, for what initial conditions is the range of x values finite for all t.

Hardcopy entries should be submitted in class by noon on Monday of next week. Answers should be concise but complete.