plugin-proj2 - Math245 Final Project Part II Due Thursday...

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Math245 Final Project - Part II Due: Thursday, Apr 23 Consider the forced-damped 2nd-order system described by the equation: d 2 y d t 2 + 2 a d y d t + ( a 2 + b 2 ) y = ( t - t 0 ) + ( t - t 1 ) , y (0) = y 0 (0) = 0 . The system initially at rest is first excited by an impulse of strength f at t = t 0 ( > 0). The system starts to oscillate immediately after the first impulse forcing. After exactly one cycle of oscillation (i.e., at t = t 1 ) the system is, again, excited by another impulse of strength K , and this impulse is designed to bring the system to rest thereafter (ie., y = 0 for t t 1 ). 1. Solve the initial value problem analytically for arbitrary values of a , b , f , t 0 , K and t 1 . Leave the answer in terms of these parameters. 2. Determine the strength K of the second impulse and its timing t 1 in terms of a , b , f and t 0 . That is, find K and t 1 to render the response to rest ( y = 0) after exactly one cycle of oscillation ( t t 1 ) following the first impulse input ( t - t 0 ).
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