Here is the problem:
A spring is such that a 2 pound weight stretches it 6 inches. There is a damping force present with magnitude the same as the magnitude of the instantaneous velocity. An impressed force f(t) = 2 sin 8t, acts on the spring. At t= 0, the weight is released from a point 3 inches below equilibrium. Find its position function.
I'm not sure if this is correct, but as far as setting up the initial differential equation, I think it is like this:
(1/16)x'' + x' + (1/3)x = 2sin8t
Is this differential equation correct? If so, can someone show step by step how to solve this using differential operators (the annihilator method) or LaPlace transforms, and how to use that to get the position function?