ISSUES RELATED TO THE PROBLEM

This problem shows students a famous identity often used in working with steady state solutions of 2nd order differential equations. The identity takes a function consisting of a sine and a cosine and re-writes it as either a sine or cosine with an amplitude and phase shift. (The problem emphasizes the amplitude feature). This identity leads directly to frequency response, and particularly resonance, which is a prominent feature of the mathematical model. Note that the solution to the differential equation is given. There is no solving of differential equations in the problem.

THE IDENTITY IS CLEARLY MARKED AS A STEP IN THE SUGGESTED SOLUTION.