The Hardest Exam I Ever Took at MIT in Physics

I only ever took one physics course as an undergraduate and I remember precisely one question from the final. To the best of my recollection (this was over 5 years ago now so I could have forgotten something), it was: suppose a metal cylinder of radius r, height h, and mass μ is suspended on a spring of length L with spring constant k in a cylindrical container or radius R that is filled with a fluid with viscosity η up to the half-way mark on the metal cylinder. Assuming the mass is given an initial downward velocity v, derive the equation of motion.

I’m pretty sure I could work it out now if I really wanted to — and probably solve the equation, too — but, needless to say, I did not finish that question at the time.