74 Dirac Delta Functions: Problem 5
Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function.
y'' + 16π²y = 4πδ(t - 4), y(0) = 0, y'(0) = 0.
a. Find the Laplace transform of the solution.
Y(s) = L {y(t)} =
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 < ∞.