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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 Laplace Transform of g(t) which has value (t-1)3 for t>1 and 0 for t<1.
2. If f(t) = eat sin(bt), then its Laplace transform is given by?
3. Initial value theorem states that ___________
4. Find the \(L^{-1} (\frac{1}{s(s+4)^\frac{1}{2}})\), give the answer in terms of error function.
5. Solve the Ordinary Diferential Equation using Laplace Transformation y’’’ – 3y’’ + 3y’ – y = t2 et when y(0) = 1, y’(0) = 0 and y’’(0) = 2.
6. While solving an Ordinary Differential Equation using the unilateral Laplace Transform, it is possible to solve if there is no function in the right hand side of the equation in standard form and if the initial conditions are zero.
7. If f(t) = coshat, its Laplace transform is given by?
8. Find the laplace transform of t5⁄2.
9. Find the value of \(\int_0^{\infty} tsin(t)cos(t)\).
10. If f(t) = 1, then its Laplace Transform is given by?
11. Find the \(L^{-1} (\frac{1}{(s+2)^4})\).
12. Find the laplace transform of f(t), where
f(t) = 1 for 0 < t < a
-1 for a < t < 2a
13. Value of \(\int_{-\infty}^\infty e^t \,Sin(t) \,dt\) = ?
14. If f(t) = tn where, ‘n’ is an integer greater than zero, then its Laplace Transform is given by?
15. Transfer function may be defined as ____________
16. Take Laplace Transformation on the Ordinary Differential Equation if y’’’ – 3y’’ + 3y’ – y = t2 et if y(0) = 1, y’(0) = b and y’’(0) = c.
17. Find the equation of transfer function which is defined by y(t)-∫0t y(t)dt + d⁄dt x(t) – 5Sin(t) = 0.
18. Solve the Ordinary Differential Equation by Laplace Transformation y’’ – 2y’ – 8y = 0 if y(0) = 3 and y’(0) = 6.
19. If f(t) = sinhat, then its Laplace transform is?
20. If f(t) = tsin(at) then its Laplace Transform is given by?
21. Laplace transform any function changes it domain to s-domain.
22. Find the inverse laplace transform of \(\frac{s}{(s^2+ 4)^2}\).
23. Find the laplace transform of f(t), where f(t) = |sin(pt)| and t>0.
24. Find the inverse lapace of \(\frac{(s+1)}{[(s+1)^2+4][(s+1)^2+1]}\).
25. Find the \(L^{-1} (\frac{s}{2s+9+s^2})\).

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