ET382 Signals and Sys Theory and Lab

W4 Assignment "HW4 “The Laplace Transform"

HW4 – The Laplace Transform

• Read Chapter 3 in the textbook Signals and Systems Using MATLAB.>


• Read the Lecture “W4 Lecture 2 – Laplace Transform”.

• Download and review the supplemental questions.

• Work the following six problems below for submission.

• Submit homework solutions via Assignment Upload Tool. Show all work for full credit.

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1.     The Laplace transform of e-10t u(t) is?

2.     The Laplace transform of (t2cosωt) u(t) is?

3.     By using the Laplace transform, compute the convolution x(t) * v(t) of the two signals? where x(t)=e-3t u(t) and v(t) = (5sint )u(t)

4.     Compute the inverse Laplace transform of X(s) = (3s2 + 2s + 1)/(s3 + 5s2 + 8s + 4)?

5.     Use Laplace transforms to compute the solution to the differential equation given below?

Where y(t)=0 ;y(t)=1

6.     Determine the final value of X(s) = (3s2 + 4s + 1)/(s4 + 3s3 + 3s2 + 2s)?