Consider an LC-Series circuit with inductance L = 3 Henry and capacitance C = Faraday. Neglect any resistance in the 12 circuit. (a) Find the differential equation y = f(y, y) satisfied by the function y, the electric current in the circuit. Write y for y(t) and yp for y' (t). y' = -4y Σ (b) Find r1, 12, roots of the characteristic polynomial of the equation above. 1,221,-21 Σ (b) Find a set of real-valued fundamental solutions to the differential equation above. y₁ (t) = cos(2t) Σ Σ y2(t)=sin(2t) (c) If the initial current in the circuit is y(0) = -2√3 Ampere with initial time derivative y'(0) = 4 Ampere/sec, find the amplitude A > 0 and the phase shift Є (-, ] of the current in the circuit. A = 4 ΣΦ = M