Network Theory Questions and Answers – Operational Transforms

This set of Network Theory Multiple Choice Questions & Answers (MCQs) focuses on “Operational Transforms”.

1. The Laplace transform of kf(t) is?
a) F(s)
b) kF(s)
c) F(s)/k
d) k2 F(s)
View Answer

Answer: b
Explanation: Operational transforms indicate how mathematical operations performed in either f(t) or F(s) are converted into the opposite domain. Linearity property states that L (kf (t)) = kF (s).

2. The Laplace transform of f1 (t) + f2 (t) is?
a) F1(s) + F2(s)
b) F1(s) – F2(s)
c) F1(s) – 2F2(s)
d) F1(s) + 2F2(s)
View Answer

Answer: a
Explanation: Addition or subtraction in time domain translates into addition or subtraction in frequency domain. L (f1 (t) + f2 (t)) = F1(s) + F2(s).

3. Find the Laplace transform of the function f (t) = 4t3 + t2 – 6t + 7.
a) 24/s4 + 2/s3 + 6/s2 + 7/s
b) 24/s4 – 2/s3 – 6/s2 + 7/s
c) 24/s4 + 2/s3 – 6/s2 + 7/s
d) 24/s4 – 2/s3 + 6/s2 + 7/s
View Answer

Answer: c
Explanation: L (4t3 + T2 -6t +7) = 4L (t3) + L(t2)-6L (t) + 7L(1) = 4×3!/s4 + 2!/s3 – 6 (1!)/(s2)+71/s = 24/s4 + 2/s3 -6/s2 + 7/s.
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4. Find the Laplace transform of the function f(t) = cos2t.
a) (2s2+4)/2s(s2-4)
b) (2s2-4)/2s(s2-4)
c) (2s2-4)/2s(s2+4)
d) (2s2+4)/2s(s2+4)
View Answer

Answer: d
Explanation: The Laplace transform of the function f(t) = cos2t is L (cos2t) = L((1+cos2t)/2) = L(1/2)+L(cos2t/2) = 1/2[L(1)+L(cos2t)] = (2s2+4)/2s(s2+4).

5. Find the Laplace transform of the function f (t) = 3t4 – 2t3 + 4e-3t – 2sin5t + 3cos2t.
a) 72/s5 – 12/s4 + 4/(s+3)+10/(s2+25)+3s/(s2+4)
b) 72/s5 – 12/s4 + 4/(s+3)-10/(s2+25)+3s/(s2+4)
c) 72/s5 – 12/s4 – 4/(s+3)+10/(s2+25)+3s/(s2+4)
d) 72/s5 – 12/s4 – 4/(s+3)-10/(s2+25)+3s/(s2+4)
View Answer

Answer: b
Explanation: L (3t4 -2t3+4e-3t – 2sin5t +3cos2t) = 3 L (t4)-2L (t3)+4L (e-3t)-2L (sin5t) + 3L (cos2t) = 72/s5) -12/s4 +4/(s+3)-10/(s2+25)+3s/(s2+4).
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6. Find the Laplace transform of eatsinbt.
a) b/((s-a)2+b2)
b) b/((s+a)2+b2)
c) b/((s+a)2-b2)
d) b/((s-a)2-b2)
View Answer

Answer: a
Explanation: The Laplace transform of sinbt is L(sinbt)=b/(s2+b2). So the Laplace transform of eatsinbt is L(exp(at) sinbt)=b/((s-a)2+b2).

7. Find the Laplace transform of (t + 2)2 et.
a) 2/(s-1)3 – 2/(s-1)2 + 4/(s-1)
b) 2/(s-1)3 – 2/(s-1)2 – 4/(s-1)
c) 2/(s-1)3 + 2/(s-1)2 + 4/(s-1)
d) 2/(s-1)3 + 2/(s-1)2 – 4/(s-1)
View Answer

Answer: c
Explanation: The Laplace transform of t2+2t+4 is L(t2+2t+4)=2/(s)3 + 2/(s)2+4/s. So the Laplace transform of (t + 2)2 et is L((t + 2)2 et) = 2/(s-1)3 + 2/(s-1)2 + 4/(s-1).
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8. Find the Laplace transform of ramp function r (t) = t.
a) 1/s
b) 1/s2
c) 1/s3
d) 1/s4
View Answer

Answer: b
Explanation: We know
Find the Laplace transform of ramp function r (t) = t.

9. Find the Laplace transform of the function f (t) = tsin2t.
a) 4s/(s2+4)2
b) -4s/(s2+4)2
c) -4s/(s2-4)2
d) 4s/(s2-4)2
View Answer

Answer: a
Explanation: The Laplace transform of the function of sin2t is L(sin2t)=2/(s2+4). So the Laplace transform of the function f (t) = tsin2t is L(tsin2t) = -d/ds [2/(s2+4)] = 4s/(s2+4)2.
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10.If u (t) = 1 for t >= 0 and u (t) = 0 for t < 0, determine the Laplace transform of [u (t) – u (t – a)].
a) 1/s(1+e(-as))
b) 1/s(1-e(-as))
c) 1/s(1+eas)
d) 1/s(1-eas)
View Answer

Answer: b
Explanation: As u (t) = 1 for t >= 0 and u (t) = 0 for t < 0, the Laplace transform of [u (t) – u (t – a)] is L[u (t)– u (t – a)] = 1/s-e(-as)1/s = 1/s (1-e(-as)).

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Manish Bhojasia - Founder & CTO at Sanfoundry
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He lives in Bangalore, and focuses on development of Linux Kernel, SAN Technologies, Advanced C, Data Structures & Alogrithms. Stay connected with him at LinkedIn.

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