In this problem, you will solve for the response of a "low pass filter" circuit element. Specifically, this element works by setting the rate at which a capacitor is charged. If a voltage signal V (t) is applied to the filter, the output voltage on the capacitor Vc(t) is defined by the following differential equation: dVc(t) dt = V (t) − Vc(t) RC (a) solve for Vc(t) given a square wave drive signal with a repetition period of T, and that takes on a value of −1 V for −T/2 < t < 0 and a value of 1 V for 0 < t < T/2. To make sure the equation is steady-state, make sure the relationship Vc(−T/2) = −Vc(0) = Vc(T/2) holds. (b) Represent Vc(t) as a Fourier sine-cosine series. (c) Comment on the waveform for when T > RC