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GATE Mechanical 2023 | Question-26

\begin{tabular}{|l|l|}
\hline Q.36 & Which one of the options given is the inverse Laplace transform of $\frac{1}{s^{3}-s} ?$ \\
& $u(t)$ denotes the unit-step function. \\
\hline

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