20. Consider the equation d²y d1² +=y=0 m for the motion of a simple harmonic oscillator. (a) Consider the function y(t) = cos ßt. Under what conditions on ß 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/B)².]

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