A mass of 7 slug stretches a spring 32/ 49 ft. At time t = 0 an external force o

ID: 2982514 • Letter: A

Question

A mass of 7 slug stretches a spring 32/49 ft. At time t = 0 an external force of f(t) = 21 cos(7t) is applied to the system. The medium through which the spring travels, offers a dampening force numerically equal to 98 times in instantaneous velocity. Find the equation of motion, and indicate both the transient and steady-state solutions.

So far I have: m=7 --> w=224. S=32/49 --> w=224=k*(32/49) --> k=343. f(t)=21cos(7t) --> F(t) = 3cos(7t). Beta = 98. 2lambda =(beta)/m = 98/7=14. omega^2 = (k/m) = 343/7 = 49.

I believe all of my starting work is correct but I went wrong somewhere getting the answers. Thanks a lot for the help!