Consider the initial value problem y?? + ?y? + y = k?(t
Question and Solution
Consider the initial value problem y?? + ?y? + y = k?(t ? 1), y(0) = 0, y? (0) = 0, where ?k? is the magnitude of an imp
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Consider the initial value problem y?? + ?y? + y = k?(t ? 1), y(0) = 0, y? (0) = 0, where ?k? is the magnitude of an impulse at t = 1 and ? is the damping coefficient (or resistance). (a) Let ? = 1 5 . Find the value of k for which the response has a peak value of 6; call this value k1. (b) Repeat part (a) for ? = 1 10 . (c) Determine how k1 varies as ? decreases. What is the value of k1 when ? = 0?
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