## Description

1. [50 points] Consider a system with the following transfer function,

H(s) = (2s+3) / (s2+5s+6)

a. Determine it’s zero-state response if the input f(t) = e-3t u(t).

b. Write down the differential equation relating output y(t) to the input

f(t).

c. Find the inverse Laplace transform of (s+2) / s(s+1)2

.

2. [30 points] For a an LTID system with the following differential equation,

2y[k+2]-3y[k+1]+y[k] = 4f[k+2]-3f[k-1],

Find the output y[k] if the input is f[k] = (4)-ku[k] and initial conditions are

y[-1] = 0 and y[-2] = 1.

3. [20 points] Find the inverse z-transform of z(-5z+22) / (z+1)(z-2)2

.