An RLC circuit, a resistor, an inductor, and a capacitor are connected across a voltage supply and satisfy

Ld²q/dt²+Rdq/dt+1/Cq=V

where L= inductance, R= resistance, C= capacitance, V= voltage, and q is the charge on the capacitor. Consider an RLC circuit with resistance 2 ohms, inductance 0.05 henrys, capacitance 0.004 farads, and an impressed voltage of V(t)=5sin(50t) provided by an alternating current generator. At t=0, the charge is 2 coulombs and the current dqdt is 3 amps.

a. Find the constansts α,β,C1,C2,A,B. Use exact values in your work and round off the final answers to at least 3 decimal places.