(Electrical circuit) Recall from Section 2.3 that the equations governing the current i(t)...

(Electrical circuit) Recall from Section 2.3 that the equations governing the current i(t) in the circuit shown, and the charge Q(t) on the capacitor are

and

respectively, where L,R,C,E,i, and Q are measured in henrys, ohms, farads, volts, amperes, and coulombs, respectively.

Let L = 2, R = 4, and C = 0.05. Solve for Q(t) subject to the initial conditions Q(0) = Q (0) = 0, where E(t) = 10e−t. Identify the steady-state solution. Give a computer plot of the solution for QQ(t) over a sufficiently long time period to clearly show the approach of Q to its steady state. (Naturally, all plots should be suitably labeled.)