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Engineering Math Practice Test: Laplace transform
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The Laplace transform is a mathematical technique that converts a function of time into a function in the frequency domain. It is an integral transform that converts a function of a real variable to a function of a complex variable.

Engineering Math Practice Test: Laplace transform
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25 Questions

1. Find the value of \(\int_0^{\infty} tsin(t)cos(t)\).
2. If f(t) = tp where p > – 1, its Laplace Transform is given by?
3. If f(t) = eat cos(bt), then its Laplace transform is?
4. If f(t) = sin(at), then its Laplace Transform is given by?
5. Find the inverse laplace transform of \(Y(s)=\frac{2s}{1-s^2}e^{-s}\).
6. With the help of _____________________ Mr.Melin gave inverse laplace transformation formula.
7. Inverse Laplace transform of \(\frac{1}{(s+1)(s-1)(s+2)}\) is?
8. If f(t) = tsin(at) then its Laplace Transform is given by?
9. Laplace transform any function changes it domain to s-domain.
10. While solving the ordinary differential equation using unilateral laplace transform, we consider the initial conditions of the system.
11. If f(t) = te-at, then its Laplace transform is?
12. If f(t) = δ(t), then its Laplace transform is?
13. Find the \(L\left (\frac{d}{dt}(\frac{sin⁡t}{t})\right)\).
14. Initial value theorem states that ___________
15. Find the poles of transfer function which is defined by input x(t)=5Sin(t)-u(t) and output y(t)=Cos(t)-u(t).
16. Find the laplace transform of et Sin(t).
17. Laplace transform of t2 sin⁡(2t).
18. If f(t) = t⁄2 a sinat, then its Laplace transform is?
19. Find the \(L^{-1} \left (\frac{(3s+9)}{(s+1)(s-1)(s-2)}\right )\).
20. Find the inverse laplace transform of \(\frac{1}{s(s-1)(s^2+1)}\).
21. Solve the Ordinary Differential Equation y’’ + 2y’ + 5y = e-t sin(t) when y(0) = 0 and y’(0) = 1.(Without solving for the constants we get in the partial fractions).
22. Laplace transform if sin⁡(at)u(t) is?
23. Find the laplace transform of y(t)=e|t-1| u(t).
24. Find the inverse laplace transform of \(\frac{s}{(s^2+ 4)^2}\).
25. Find the \(L(e^{2t} (1+t)^2)\).

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