Question

Laplace Transform

Question 1:
For the following transfer function:
H(s)= (s^2 -1)/(s^2+s+1)
Plot the poles and zeros in the s-plane and determine and sketch the inverse Laplace transform h(t ) using Matlab.

Question 2:

For the following transfer function:
H(s) = 3 + ( (s+4) / (s^2+3s+2) )
Find and sketch the inverse Laplace transform h(t) using Matlab..

Question 3:
Solve the following second order differential equation:
y\\ + 4y\ + 3y = 4 e^-3x , given that y(0) = 1 and y\ (0) = -1
and sketch the output y(t) using Matlab.