Properties of the Laplace Transform MCQ’s

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This set of Signals & Systems Multiple Choice Questions & Answers (MCQs) focuses on “Properties of the Laplace Transform”.

1. Find the Laplace transform of the signal x(t) = e-2t cos⁡(200πt)u(t).
a) \frac{s}{s^2+(200π)^2}
b) \frac{s}{s^2-(200π)^2}
c) \frac{s-2}{(s-2)^2+(200π)^2}
d) \frac{s+2}{(s+2)^2+(200π)^2}

2. Find the Laplace transform of the signal x(t) = sin⁡(\frac{t}{2})u(\frac{t}{2}).
a) \frac{1}{s^2+1}
b) \frac{s}{s^2+1}
c) \frac{2s}{(2s)^2+1}
d) \frac{2}{(2s)^2+1}

3. Find the Laplace transform of x(t) = u(t+2) + u(t-2).
a) \frac{cos⁡2s}{s}
b) \frac{cosh⁡2s}{s}
c) \frac{sinh⁡2s}{s}
d) \frac{sin⁡2s}{s}

4. Find the Laplace transform of the signal x(t) = \frac{dδ(t)}{dt}.
a) 1
b) s
c) \frac{1}{s}
d) s2

5. Find the Laplace transform for f(t) = \frac{1}{t} [e-2t – e-3t]u(t).
a) ln\left(\frac{s-2}{s-3}\right)
b) ln\left(\frac{s+2}{s+3}\right)
c) ln\left(\frac{s-2}{s+3}\right)
d) ln\left(\frac{s+2}{s-3}\right)

6. Find the final value of the function F(s) given by \frac{(s-1)}{s(s^2-1)}.
a) 1
b) 0
c) -1
d) ∞

7. Find the Laplace transform of the signal x(t) = te-αt.
a) \frac{1}{s^2}
b) \frac{1}{(s+α)^2}
c) \frac{1}{α}
d) \frac{1}{s+α}

8. Find the initial value of f(t) if F(s) = \frac{s}{(s+a)^2+ω^2}.
a) 0
b) -1
c) ∞
d) 1

9. Determine the initial value x(0+) for the Laplace transform X(s) = \frac{4}{s^2+3s-5}.
a) -1
b) 0
c) 1
d) ∞

10. Find x(∞) if X(s) is given by \frac{s-2}{s(s+4)}.
a) 1
b) -1
c) \frac{1}{2}
d) –\frac{1}{2}

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