a) State and prove second shifting theorem. Also find the inverse L.T…

Question

a) State and prove second shifting theorem. Also find the inverse L.T. of $\frac{(S^2 - 2S + 3)e^{-3s}}{(S+1)(S-1)^2}$.

b) Find the L.T. of $t^2 e^{-2t} \cos 2t$.

c) Find the inverse Fourier cosine transform of $\overline{f}(S) = \begin{cases} S^2 - 1, & 0 \le S < 1 \\ 0, & \text{otherwise} \end{cases}$

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