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GATE Mechanical 2023 | Question: 26

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

  1. $\left(-1+\frac{1}{2} e^{-t}+\frac{1}{2} e^t\right) u(t)$
  2. $\left(\frac{1}{3} e^{-t}-e^t\right) u(t)$
  3. $\left(-1+\frac{1}{2} e^{-(t-1)}+\frac{1}{2} e^{(t-1)}\right) u(t-1)$
  4. $\left(-1-\frac{1}{2} e^{-(t-1)}-\frac{1}{2} e^{(t-1)}\right) u(t-1)$

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