The response of the underdamped system is given by x(t) = Ae^-gamma omega _nt(si

Question

The response of the underdamped system is given by x(t) = Ae^-gamma omega _nt(sin (omega_d t + phi) Where A = [(v_0 + gamma omega _n x_0)^2 + (x_0 omega _d)^2/omega^2_d]^1/2 phi = tan^-1(x_0 omega _d/v_0 + gamma omega _n x_0) gamma = c/2m omega _n omega_n = squreroot k/m omega_d = omega_n squreroot 1 - gamma^2 For m = 5 kg, x_0 = 2mm, v_0 = 0 find c and k such that A = 3mm find the time it rakes to damp out the response use a 4th order Runge-Kutta method to approximate the solution for 0 lessthanorequalto t lessthanorequalto 20 and plot the results.

Explanation / Answer

The answer of following question is as follows.

The maximum value of the damper is 7

While the value of the spring is 9

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