Task 1

Evaluate Laplace transforms and their inverse using tables and partial fractions

1.   Determine the Laplace transform of each of the following

2.   Evaluate the inverse Laplace transforms of the subsequent functions

Task 2 

Solve first and second order differential equations using Laplace transforms

3.   Solve the subsequent first order differential equations using Laplace transforms

4.   Use  Laplace transform to solve the subsequent second order differential equation

Task 3 

Model and examine engineering systems and evaluate system behaviour using Laplace transforms

5.   A series LR circuit with a step input voltage will be modelled by the equation:

                i(0)=0  L, R and V are constants                    

Use Laplace transforms to show:

6.   The charge in a series LCR circuit is modeled by the equation:

Solve the equation in case when L=2 H, R=20?, C=0.02 F