Inverse Laplace Transform General Properties Questions and Answers - Sanfoundry PDF

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3/31/2021

Inverse Laplace Transform General Properties Questions and Answers - Sanfoundry

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This set of Ordinary Dierential Equations Multiple Choice Questions & Answers (MCQs) focuses on “General Properties of Inverse Laplace Transform”. 1. Find the \(L^{-1} (\frac{s+3}{4s^2+9})\). a) \(\frac{1}{4} cos(\frac{3t}{2})+\frac{1}{2} cos(\frac{3t}{2})\) b) \(\frac{1}{4} cos(\frac{3t}{4})+\frac{1}{2} sin(\frac{3t}{2})\) c) \(\frac{1}{2} cos(\frac{3t}{2})+\frac{1}{2} sin(\frac{3t}{2})\) d) \(\frac{1}{4} cos(\frac{3t}{2})+\frac{1}{2} sin(\frac{3t}{2})\) View Answer

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Inverse Laplace Transform General Properties Questions and Answers - Sanfoundry

2. Find the \(L^{-1} (\frac{1}{(s+2)^4})\). a) \(e^{-2t}×3\) b) \(e^{-2t}×\frac{t^3}{3}\) c) \(e^{-2t}×\frac{t^3}{6}\) d) \(e^{-2t}×\frac{t^2}{6}\) View Answer 3. Find the \(L^{-1} (\frac{s}{(s-1)^7})\). a) \(e^{-t} \left (\frac{t^6}{5!}+\frac{t^5}{6!}\right )\) b) \(e^t \left (\frac{t^6}{5!}+\frac{t^5}{6!}\right )\) c) \(e^t \left (\frac{t^6}{6!}+\frac{t^5}{5!}\right )\) d) \(e^{-t} \left (\frac{t^6}{6!}+\frac{t^5}{5!}\right )\) View Answer 4. Find the \(L^{-1} (\frac{s}{2s+9+s^2})\). a) \(e^{-t} \{cos(2\sqrt{2t})-sin(\sqrt{2t})\}\) b) \(e^{-t} \{cos(2\sqrt{2t})-sin(2\sqrt{2t})\}\) c) \(e^{-t} \{cos(2\sqrt{2t})-cos(\sqrt{2t})\}\) d) \(e^{-2t} \{cos(2\sqrt{2t})-sin(2\sqrt{2t})\}\) View Answer 1} \left (\frac{(s+1)}{(s+2)(s+3)}\r

)\).

2e-3t-e-2t b) 3e-3t -e-2t c) 2e -3t-3e -2t d) 2e-2t -e-t

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Inverse Laplace Transform General Properties Questions and Answers - Sanfoundry

Answer: a Explanation: In the given question, \(L^{-1} \left (\frac{(s+1)}{(s+2)(s+3)}\right )=L^{-1} \left (\frac{2(s+2)-(s+3)}{(s+2)(s+3)}\right )\) =\(L^{-1} \left (\frac{2}{(s+3)}\right )+L^{-1} \left (\frac{1}{(s+2)}\right )\) =2e -3t-e -2t. advertisement

6. Find the \(L^{-1} \left (\frac{(3s+9)}{(s+1)(s-1)(s-2)}\right )\). a) e-t+6et+5e2t b) e-t -et+5e2t c) e -3t-6e t+5e 2t d) e-t -6et+5e2t View Answer Answer: d Explanation: In the given question, \(L^{-1} \left (\frac{(3s+9)}{(s+1)(s-1)(s-2)}\right )\) =\(L^{-1} \left (\frac{1}{(s+1)}\right )-6L^{-1} \left (\frac{-6}{(s-1)}\right )+5L^{-1} \left (\frac{-6}{(s2)}\right ) \)————-Using properties of Partial Fractions -t

t

2t

=e -6e +5e . 7. Find the \(L^{-1} (\frac{1}{(s^2+4)(s^2+9)})\). a) \(\frac{1}{5} \left (\frac{sin(2t)}{2}-\frac{sin(t)}{3}\right )\) b) \(\frac{1}{5} \left (\frac{sin(2t)}{2}+\frac{sin(3t)}{3}\right )\)

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Inverse Laplace Transform General Properties Questions and Answers - Sanfoundry

d) \(\frac{1}{5} \left (\frac{sin(2t)}{2}-\frac{sin(3t)}{3}\right )\) View Answer 8. Find the \(L^{-1} \left (\frac{s}{(s^2+1)(s^2+2)(s^2+3)}\right )\). a) \(\frac{1}{2} cos(t)-cos(\sqrt3t)-\frac{1}{2} cos(\sqrt3t)\) b) \(\frac{1}{2} cos(t)+cos(\sqrt2t)-\frac{1}{2} cos(\sqrt3t)\) c) \(\frac{1}{2} cos(t)-cos(\sqrt2t)-\frac{1}{2} cos(\sqrt3t)\) d) \(\frac{1}{2} cos(t)+cos(\sqrt2t)+\frac{1}{2} cos(\sqrt3t)\) View Answer 9. Find the \(L^{-1} \left (\frac{s+1}{(s-1)(s+2)^2}\right )\). a) \(\frac{2}{7} e^t-\frac{2}{9} e^{-2t}+\frac{1}{3} e^{-2t}×t\) b) \(\frac{2}{9} e^t-\frac{2}{9} e^{-2t}+\frac{1}{3} e^{-2t}×t\) c) \(\frac{2}{9} e^t-\frac{2}{9} e^{-3t}+\frac{1}{3} e^{-2t}×t\) d) \(\frac{2}{9} e^t-\frac{2}{9} e^{-2t}+\frac{1}{3} e^{-2t}\) View Answer

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10.

The

\(L^{-1}

\left

(\frac{3s+8}{s^2+4s+25}\right

)\)

is

\(e^{-st}

(3cos(\sqrt{21}t+\frac{2sin(\sqrt{21}t)}{\sqrt{21}})\). What is the value of s? a) 0 b) 1 c) 2

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Inverse Laplace Transform General Properties Questions and Answers - Sanfoundry

Answer: c Explanation: In the given question, \(L^{-1} \left (\frac{3s+8}{s^2+4s+25}\right )=L^{-1} \left (\frac{3(s+2)+2}{(s+2)^2+21}\right )\) By the rst shifting property =\(e^{-2t} L^{-1} \left (\frac{3s+2}{s^2+21}\right )\) =\(e^{-2t} L^{-1} \left (\frac{3s}{s^2+21}\right )+e^{-2t} L^{-1} \left (\frac{2}{s^2+21}\right )\) =\(e^{-2t} (3cos(\sqrt{21}t+\frac{2sin(\sqrt{21}t)}{\sqrt{21}})\). Sanfoundry Global Education & Learning Series – Ordinary Dierential Equations. To practice all areas of Ordinary Dierential Equations, here is complete set of 1000+ Multiple Choice Questions and Answers. Participate in the Sanfoundry Certication contest to get free Certicate of Merit. Join our social networks below and stay updated with latest contests, videos, internships and jobs! Telegram | Youtube | LinkedIn | Instagram | Facebook | Twitter | Pinterest « Prev - Ordinary Dierential Equations Questions and Answers – Laplace Transform of Periodic Function » Next - Laplace Transform Questions and Answers – Convolution

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn

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