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Question 3 Consider an LC circuit, with a single inductor (inductance L) and a single capacitor (capacitance C). Complete each of the following: 1. Use Kirchoff's laws to write down a differential equation to model this circuit, and explain why this equation is in the form of simple harmonic motion 2. Based on the form of the equation, determine the angular fre- quency w 3. Show that the function q(t) = Q cos (wt + 0) is a solution to the differential equation in Part 1. for all time / by direct substitution (show LHS - RHS after substitution), where Q is a constant (amplitude of the oscillating charge value)