# 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.
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)?

# Lab4 – The Laplace Transform

• Watch video entitled “Module 4 – Laplace Transform in MATLAB”
• Work the two problems below.
• Include answers for Problems and include MATLAB coding along with any output plots that support solutions into a Word document entitled “Lab4_StudentID”.  Where your student id is substituted in the file name.
• Upload file “Lab4_StudentID”.

Activity 1:

Work the problems at the end of Chapter 3: Problems 3.31(b), 3.32(a), and 3.32(b) using MATLAB.

Activity 2:

A linear time-invariant continuous-time system has the impulse response below:

h(t) =[cos 2t + 4 sin 2t]u(t)

1. Determine the transfer function H(s) of the system.  Use the Laplace transform pairs table for this.
2. Plot the system impulse response using Matlab.
3. The input, x(t) is defined as  for x ≥ 0.  Find X(s) using the tables.
4. Compute the output response Y(s).
5. Compute y(t) using the Laplace Transform pairs and plot y(t).
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