Engineering Math 2: Laplace Transform 1 - Tutorial Questions
Laplace Transform
1. Use the table of Laplace transforms to determine y- (s) for each of the following functions y(t).
a. 7e-(t+√2)
b. (t + 2)2
c. 2t3 + e 2t+5
d. 2t5 + 4t2 + 3t + 2
2. Find the Laplace transform. of the function
y(t) = e3teπt(1 + 2(cos2 t + sin2 t))
3. Find the Laplace transform. of y(t) = sin2 t
4. Find the Laplace transform. of the function y(t) = t sin 4t
5. Determine the Laplace transform. of the function: y(t) = t 2 sin 4t
6. L{cosh at cos at}
7. L{sinh at sin at}
8. L{cosh(2t) sin(3t)}
Inverse Laplace Transform
9. Find the function y(t) whose inverse Laplace transform. is given by:
10. Using Laplace transform. table, determine y(t) for each of the following functions:
11. Use the Laplace transform. table to determine the function y(t) for each of the following
functions:
Hint: Use completing the square technique to evaluate the denominator, create two different fractions to cast problem in a form. that will allow easy usage of the Laplace transform. table.
Further Problems on Laplace Transform
12. Use the table of Laplace transform. to determine y- (s) for each of the following functions of y(t) .