Consider the damped spring-mass system with m = 1, k = 5, c = 2, and F(t) = 8 cos t. (a)

Chapter 8, Problem 32

(choose chapter or problem)

Consider the damped spring-mass system with m = 1, k = 5, c = 2, and F(t) = 8 cos t. (a) Determine the transient part of the solution and the steady-state solution. (b) Determine the value of that maximizes the amplitude of the steady-state solution and express the corresponding solution in the form yp(t) = A0 cos(t ), for appropriate constants A0,, and . 33. Consider the spring-mass system whose motion is governed by the differential equation d2 y dt2 + 2 dy dt + 5y = 4et cos 2t. (a) Describe the variation with time of the applied external force. (b) Determine the motion of the mass. What happens as t ? 34. Consider the spring-mass system whose motion is governed by the differential equation d2 y dt2 + 16y = 130et cost. Determine the resulting motion, and identify any transient and steady-state parts of your solution.