1. The problem statement, all variables and given/known data Consider a mass connected to a spring of stiness k. (a) Use conservation of energy to write down a first order differential equation obeyed by the mass. (b) Find the time t for the mass to move from the origin at t = 0 out to a position x assuming that at t = 0 it has initial speed dx/dt = v0. (c) Use the above to show that the period of motion is T = 2∏sqrt(m/k) 2. Relevant equations Us = .5kx^2 K = .5mv^2 3. The attempt at a solution a) I just set up a initial and final conservation of energy I figured that I'd just set Us = K and make v = (dx/dt). That'd give me a natural log in my answer, which doesn't seem to make much sense. Everything else doesn't seem to be too hard once I get part a.