ET 382 Week 4 Homework

  

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 (in the section “Execution/Results”).

Circuit design:

No circuits were designed in the process of executing this assignment.

Execution/Results:

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

Solve differential equation d^2y/(dt)^2 + dy/dt = 8y

Boundary conditions y(0)=0; y'(0)=1

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