2. We consider the differential equation satised by the capacitor voltage \"cm in the transient response of an RLC circuit: [2+2 +3 + 3 +l=11 marks] R L ' 1L(t) d2?) we do '3 +\" +w3vc=wumnm (I) + at? Q dt ' Vc(t) where can is the undamped frequency, Q is the quality factor, pin is the voltage source. Background: https : / fen. wikipedia. org/wiki/RLC_Circuit (a) Consider a circuit with mu 2 10 (radfs) , C = 1F, Q = 0.5 and with the voltage source set to zero, so that 1511(3) = 0. Find the general solution for the capacitor voltage mist). (b) A circuit is underdamped when the transient response includes oscillatory solutions. For the system given in {1%}, how should we change Q in order for the circuit to be underdamped should we increase, decrease, or keep Q the same? (c) For the circuit in ., nd v.3(t) for initial conditions com) 2 2, and 336(0) = 5A. Here c is the current through the capacitor, and it is related to Ur.- by a}: = 0%. (d) A voltage source is added to the circuit, such that \"in (t) = % sin(5t). Find a particular solution to {m}, with the values of the constants 0, mg, Q as in .. (c) Find the general solution to {D with 0,010, Q as in ., and um as in