Consider the following inverse Laplace transform problems.

(a) Given the Laplace transform

which is not proper, determine the amplitude of the δ(t)and dδ(t)/dt terms in the inverse signal y(t).

(b) Find the inverse Laplace transform of

Can you use the initial-value theorem to check your result? Explain.

(c) The inverse Laplace transform of

should be of the form x(t) = [Ae^ˆ’t + B + Ce^ˆ’2t] u(t). Find the values of A,B and C. Use the MATLAB function ilaplace to get the inverse and to plot it.

s* + 25 + 1 Y (s) = s + 4s + 5s +2 s - 3 Z(s) = (s + 1)(s + 2)