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# HW and LAB

**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.

- The Laplace transform of e-10t u(t) is?
- The Laplace transform of (t2cosωt) u(t) is?
- 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)
- Compute the inverse Laplace transform of X(s) = (3s2 + 2s + 1)/(s3 + 5s2 + 8s + 4)?
- Use Laplace transforms to compute the solution to the differential equation given below?
Where y(t)=0 ;y(t)=1

- 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)

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