Consider the equationfor the motion of a simple harmonic oscillator.(a) Consider the funct...

Consider the equation

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?

(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) associated to this solution. [Hint: Consider the quantity y2 + (v/β)2.]