Which one of the options given is the inverse Laplace transform of \frac{1}{s^{3}−s}? 𝑢(𝑡) denotes the unit-step function.

Correct Answer is : (−1+12e−t+12et)u(t)

(−1 + \frac{1}{2}e^{−t} + \frac{1}{2}e^{t}) u(t)

(\frac{1}{3}e^{−t}−e^{t}) u(t)

(−1 + \frac{1}{2}e^{−(t−1)} + \frac{1}{2}e^{(t−1)}) u(t−1)

(−1−\frac{1}{2}e^{−(t−1)}−\frac{1}{2}e^{(t−1)}) u(t−1)

GATE Mechanical Engineering (ME) 2023 Shift 1 Solved Paper

Question : 36 of 65

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Which one of the options given is the inverse Laplace transform of

\;{1}/{s^{3}−s}

? 𝑢(𝑡) denotes the unit-step function.

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