The Laplace Transform HW

• 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 (t2cos ωt ) 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) =  (5sin t )u(t)

4. Compute the inverse Laplace transform of X(s) = 3s2+2s+1s3+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+1s4+3s3+3s2+2s  ?

**PLEASE SEE ATTACHMENTS**