# Thanks Consider the system y" 2by + y 0 with initial conditions y(0) 0, y (0)...

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Consider the system y" 2by + y 0 with initial conditions y(0) 0, y (0) = Uo. Assume y represents the position of an object (a) In the case of critical damping find the value of Uo such that the output achieves a maximum position of D Hint: you may see my name popping up somewhere!!! Recall that the critically damped case provides the fastest decay (b) Assume now an overdamped system such that b rate. Despite this show that the maximum in this scenario (i.e. when b) occurs before it does in part (a)

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