Note: Every time you use the Laplace transform and get a function in the s-domain, remember to write for which s that function is valid.
Task 1
Determine the Laplace transform of the functions:
e) Rewrite the function using the Heaviside’s function and determine the Laplace transform of
the function:
Task 2
Determine the inverse Laplace transform of the functions:
When using s-shift, determine the inverse Laplace transform of the functions:
Task 3
a) Determine the convolution of the function using the Laplace transformation. You will need the
result from problem 2b)
b) Solve for x (t) using the Laplace transform. Hint: identify the convolution in the equation.
Task 4
Use the Laplace transform to solve the differential equation
with the initial values
