Determine Laplace transforms and their inverse using tables and partial fractions:

problem 1: Find the Laplace transform of each of the following:

problem 2: Find the inverse Laplace transforms of the following functions:

Solve first and second order differential equations using Laplace transforms.

problem 3: Solve the given first order differential equations by using Laplace transforms.

problem 4: Use Laplace transform to solve the given second order differential equation:

Model and analyse engineering systems and determine system behaviour using Laplace transforms

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

Use Laplace transforms to show:

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

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