Homework: HW 4.10 Score: 0 of 1 pt X) 4.10.13 A mass weighing 96 lb is attached

Question

Homework: HW 4.10 Score: 0 of 1 pt X) 4.10.13 A mass weighing 96 lb is attached to a spring hanging from the ceiling and comes to rest at its equilibrium position. At time t-0, an external force of F() 3cos 6t lb is Save 3 of 4 (3 complete) HW Score: 25%, 1 of 4 pts Question Help applied to the system. If the spring constant is 20 lb/ft and the damping constant is 4 lb-sec/ft, find the steady-state solution for the system. Use g 32 ft/sec2 The steady-state solution is y(t) Enter your answer in the answer box and then click Check Answer.

Explanation / Answer

mass = 96lb/(32 ft/s^2) = 3
damping = 4
k = 20

3y'' + 4y' +20y = 3cos(6t)

solution to homogenous is y(t)=e^(-2t/3)[a*cos(2.49t) + b*sin(2.49t)
solution to particular equation is 9/1040sin(6t) - 33/1040cos(6t) using undetermined coefficients.

y(t) = e^(-2t/3)[a*cos(2.49t) + b*sin(2.49t) +  9/1040sin(6t) - 33/1040cos(6t)

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