Engineering Mathematics Questions and Answers – Laplace Transform by Properties – 3

This set of Engineering Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Laplace Transform by Properties – 3”.

1. Time domain function of \(\frac{s}{a^2+s^2}\) is given by?
a) Cos(at)
b) Sin(at)
c) Cos(at)Sin(at)
d) Sin(t)
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2. Inverse Laplace transform of \(\frac{1}{(s+1)(s-1)(s+2)}\) is?
a) –¹⁄₂ e^t + ¹⁄₆ e^-t + ¹⁄₃ e^2t
b) –¹⁄₂ e^-t + ¹⁄₆ e^t + ¹⁄₃ e^-2t
c) ¹⁄₂ e^-t – ¹⁄₆ e^t – ¹⁄₃ e^-2
d) –¹⁄₂ e^-t + ¹⁄₆ e^-t + ¹⁄₃ e^-2
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3. Inverse laplace transform of \(\frac{1}{(s-1)^2 (s+5)}\) is?
a) ¹⁄₆ e ^{– t} – ¹⁄₃₆ e^t + ¹⁄₃₆ e^-5t
b) ¹⁄₆ e^tt – ¹⁄₃₆ e^t + ¹⁄₃₆ e^-5t
c) ¹⁄₆ e^-tt² – ¹⁄₃₆ e^-t + ¹⁄₃₆ e^5t
d) ¹⁄₆ e^-t t-¹⁄₃₆ e^-t + ¹⁄₃₆ e^5t
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4. Find the inverse laplace transform of \(\frac{1}{(s^2+1)(s – 1)(s + 5)}\).
a) ¹⁄₁₂ e^t – ¹⁄₁₃ Cos(-t) – ¹⁄₁₂ Sin(-t) – ¹⁄₁₅₆ e^-5t
b) ¹⁄₁₂ e^-t – ¹⁄₁₃ Cos(t) – ¹⁄₁₂ Sin(t) – ¹⁄₁₅₆ e^5t
c) ¹⁄₁₂ e^t – ¹⁄₁₃ Cos(t) – ¹⁄₁₂ Sin(t) – ¹⁄₁₅₆ e^-5t
d) ¹⁄₁₂ e^t + ¹⁄₁₃ Cos(t) + ¹⁄₁₂ Sin(t) + ¹⁄₁₅₆ e^-5t
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5. Find the inverse laplace transform of \(\frac{s}{(s^2+ 4)^2}\).
a) ¹⁄₄ sin(2t)
b) ^t2⁄₄ sin(2t)
c) ^t⁄₄ sin(2t)
d) ^t⁄₄ sin(2t²)
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6. Final value theorem states that _________
a) x(0)=\(\lim_{x\rightarrow ∞} sX(s)\)
b) x(∞)=\(\lim_{x\rightarrow ∞} sX(s)\)
c) x(0)=\(\lim_{x\rightarrow 0} sX(s)\)
d) x(∞)=\(\lim_{x\rightarrow 0} ⁡sX(s)\)
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7. Initial value theorem states that ___________
a) x(0)=\(\lim_{x\rightarrow ∞} sX(s)\)
b) x(∞)=\(\lim_{x\rightarrow ∞} sX(s)\)
c) x(0)=\(\lim_{x\rightarrow 0} sX(s)\)
d) x(∞)=\(\lim_{x\rightarrow 0} ⁡sX(s)\)
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8. Find the value of x(∞) if \(X(s)=\frac{2s^2+5s+12/s}{s^3+4s^2+14s+20}\).
a) 5
b) 4
c) ¹²⁄₂₀
d) 2
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9. Find the value of x(0) if \(X(s)=\frac{2s^2+5s+12/s}{s^3+4s^2+14s+20}\).
a) 5
b) 4
c) 12
d) 2
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10. Find the inverse lapace of \(\frac{(s+1)}{[(s+1)^2+4][(s+1)^2+1]}\).
a) ¹⁄₃ e^t [Cos(t) – Cos(2t)].
b) ¹⁄₃ e^-t [Cos(t) + Cos(2t)].
c) ¹⁄₃ e^t [Cos(t) + Cos(2t)].
d) ¹⁄₃ e^-t [Cos(t) – Cos(2t)].
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11. Find the inverse laplace transform of \(Y(s)=\frac{2s}{1-s^2}e^{-s}\).
a) -e^{-t + 1} + e^{t – 1}
b) -e^{-t + 1} – e^{t + 1}
c) -e^{-t + 1} + e^{t + 1}
d) -e^{-t + 1} – e^{t – 1}
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12. Find the inverse laplace transform of \(\frac{1}{s(s-1)(s^2+1)}\).
a) ¹⁄₂ e^-t + ¹⁄₂ Sin(-t) – ¹⁄₂ Cos(-t)
b) ¹⁄₂ e^t + ¹⁄₂ Sin(t) – ¹⁄₂ Cos(t)
c) ¹⁄₂ e^t + ¹⁄₂ Sin(t) + ¹⁄₂ Cos(t)
d) ¹⁄₂ e^t – ¹⁄₂ Sin(t) – ¹⁄₂ Cos(t)
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