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Engineering Math 2: Laplace Transform. 2 - Tutorial Questions

1.   Solve the flowing initial value problems using Laplace transform table and partial fraction decomposition techniques (where necessary).

2.   Find the Laplace transform of

3.   L{u3(t) sin 3(t 一 3)}

Note: Heaviside unit step function may be denoted by uc (t), this is the same as u(t 一 C)

7.   Determine the expression f(t) and sketch the graph of f(t) up to f(4) if the Laplace

transform of f(t) is given by:

8.   Determine the expression f(t) and sketch the graph of f(t) up to f(4) if the Laplace

transform of f(t) is given by:

9.   Solve for x(t) in the following differential equation and sketch the input H(t 一 4) and the response graph of x(t) up to t = 6.

10. Solve for x(t) in the following differential equation with an impulse input: