1. Express the following function in terms of units step functions and find its Laplace transform:
\begin{equation*}
f(t) = \begin{cases}
0, & 0 < t < 2 \\
3, & 2 < t < 5 \\
0, & t > 5
\end{cases}
\end{equation*}
[3]
2. Find the inverse Laplace transform for $\frac{2s^2 - 3s + 5}{s^2(s^2 + 1)}$.
[3]
3. Solve the given initial value problems using the Laplace transform: $y'' + y = \cos t$, $y(\pi) = 0$, $y'(\pi) = 0$. [4]
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