An LR circuit, modeled by the initial value problemhas the solutionwhich is made up of a t...

An LR circuit, modeled by the initial value problem

has the solution

which is made up of a transient response, −(l/5)e_t, and a steady-state response, (2/5) sin 2t + (1/5) cos 2t.

(a) On one plot, sketch the graph of the solution in black, the transient response in red, and the steady-state response in blue.

(b) Create a second plot that contains the steady-state response in blue. Use your numerical solver to superimpose the solutions of I' + I = cos 2t on your plot for the initial conditions 7(0) = −1, −0.5,…, 1. Explain the behavior of the solutions in terms of the steady-state and transient response.