Problems:

Find the Laplace transforms of the following functions of time: (which are defined for and null for )

1. 
2. 
3. 

   Obtain the inverse Laplace tranforms of

4. 
5. 
6. 
7. 
8. 
9. 

   and verify by using "impulse" that your analytical answers are correct.

   In the final problem, use the commands "rmodel", "series" and "parallel".

10. Use the models in Problem 5 and Problem 7. Connect them in a) series, b) parallel. Find the poles and zeros of the resulting transfer functions. Compute and plot the impulse response of each. For each transfer function do a partial fraction expansion. Interpret the impulse responses in terms of the partial fraction expansion.