Hi. So...

Suppose that an object weighing 4lbs stretches a spring 2 inches. The object is displaced an additional six inches below the equilibrium position and then released. The object is in a medium that exerts a damping force nemuerically equal to 2 times the instantaneous velocity. Determine the equation of motion.

So, Here I know that since F=ks by Hooke's Law, we can determine k as follows:

.

Now, since from newton's second law we know that

, where

and

and we can equate this to the sum of the restoring force of the spring and the resistant force of the medium so that

Am I on the right track?