In the circuits shown below, R = R₁ =3, R₂ = 1, C=% and L=1. The output of the left circuit is

Vo. The matrix, A, is given by

1)

2)

3)

4)

5)

Vs

A =

L

ro

Find the impulse response of the circuit on the left.

Find the step response of the circuit on the left-that is, find the zero-state response assuming

that the input is a unit step function. You must use the convolution integral and your solution

to part 1 to do this.

Redo part 2-that is, find the step response-without using convolution.

For the circuit on the right, solve for I and V₁ as functions of Ve, I, and Vs.

Show that the matrix, A, solves its own characteristic equation.

R₁

R

0 2

-1 -3

+

Vs

+V₁

R₂

Ic

+