Ifthe term cu'(t) is added to the left side ofthe motion equation in Exercise 7, the

Chapter 4, Problem 12

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Ifthe term cu'(t) is added to the left side ofthe motion equation in Exercise 7, the resulting differential equation describes a spring-mass system that is damped with damping constant c ^ 0. The solution to this equation when the system is initially at rest is Fq u(t) = Citf'1 ' + C2er2' + -T-^r ^^5 r (ecu sin cut + m (cur, - cu2 ) cos cut) , c^a>I +m z {(i>Q-a)z y where -c + Jc 1 4(ohn2 -c Jc 1 Aa&m2 r\ = ; and r2 = 1 . 2m 2m a. Let m = \, k = 9, Fq = 1, c = 10, and cu = 2. Find the values of cq and C2 so that M(0) = M'(0) = 0. b. Sketch the graph of u{t) for t g fO, 27t1 and approximate J0 T u(t) dt to within 10-4