1. The problem statement, all variables and given/known data A 50kg mass is attached to a spring and hung from an overhead beam. The Force on the spring when extended 2 meters from rest is 50N. The resting length of the spring is 1m. 1) Obtain the ODE to solve for the velocity as a function of position (NOT time) 2) Solve the ODE if the spring is dropped from it's rest length of 1m 2. Relevant equations F= -kx, F=ma, a(t) = dv/dt, v(t)=dx/dt, F(2) = -50N, V(x0) = 0, x = distance below the overhead beam) 3. The attempt at a solution I am mostly having trouble coming up with an equation to solve. We are specifically forbidden from using second order methods to solve. I know logically that it's a periodic function since the spring oscillated up and down once released. I also know (as per my professor) that the solution v(x) will NOT be a periodic function. My attempted equation is: dv/dx = -kx+mg I was able to solve that (presumably incorrect) equation and get -k/2m x2 +gx +c Am I on the right track or have I completely missed a key concept somewhere. Thanks.