Question

Problem 1 Given the circuit shown below in Fig. 1.1: Write the ordinary differential equation (ODE) for the capacitor voltage. Find the zero-state unit step responses of v(t) and i(t) if vs-u(t) V using each of the following three methods of solving the ODE: a. b. i. ii. Solve the ODE by integrating for the solution; Solve the ODE by assuming homogeneous and particular solutions; Solve the ODE by using the general form solution for a 1st order ODE. iii. Zero-state means that all initial conditions are zero. The unit step input is: u(t) 0 for t< 0 -1 fort0 Sketch the responses of v(t) and i(t) showing t-0, τ and oo 3 S2 U) 6 52 U) Fig. 1.1

Answer 1