(a) Text, take a rectangular wave of area 1 from 1 to 1 + k. Graph the responses for a sequence of values of k approaching zero, illustrating that for smaller and smaller k those curves approach the curve shown in Fig. 134. If your CAS gives no solution for the differential equation, involving k, take specific k€™s from the beginning.
(b) Experiment on the response of the ODE (or of another ODE of your choice) to an impulse δ(t - α) for various systematically chosen α (> 0); choose initial conditions y(0) ‰  0, y' (0) = 0. Also consider the solution if no impulse is applied. Is there a dependence of the response on α? On b if you choose bδ(t - α)? Would -δ(t - α^ˆ¼) with α^ˆ¼ > α annihilate the effect of δ(t - α)? Can you think of other questions that one could consider experimentally by inspecting graphs?

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y(t) 0.2 0.1- 3 5 Response to a hammerblow in Example 2 Fig. 134.