Consider the following initial value problem, in which an input of large amplitude and short duration has been idealized as a delta function: x" + 167x = . 4πδ(t-1 ), 1(0) = 0, z'(0) = 0. %3D In the following parts, use h(t – c) for the Heaviside function h.(t) if necessary. a. Find the Laplace transform of the solution. 4ле L{x(t)}(s) = s2 + 1672 b. Obtain the solution x(t). x(t) = c. Express the solution as a piecewise-defined function and think about what happens to the graph of the solution at t = 1. if 0

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