Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function. y" + 9n²y = 3nd(t – 4), y(0) = 0, y'(0) = 0. a. Find the Laplace transform of the solution. Y(s) = L{y(t)} = = 3pie^(-4s)/(s^2+(3pi)^2) b. Obtain the solution y(t). y(t) = c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 4. y(t) = if 0 ≤ t < 4, if 4 < t <∞.

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