Consider the equation d 2 dt2 + k m y = 0 for the motion of a simple harmonic oscillator. (a) Consider the function y(t) = cos βt. Under what conditions on β is y(t) a solution to the differential equation? (b) What initial condition (t = 0) in the yv-plane corresponds to this solution? (c) In terms of k and m, what is the period of this solution? (d) Sketch the solution curve in the yv-plane that corresponds to this solution.