1. The problem statement, all variables and given/known data A particle of mass m is subject to a force F (x) = -kx. The initial position is zero, and the initial speed is v0. Find x(t). 2. Relevant equations F = m*v*dv/dx = -kx v = dx/dt 3. The attempt at a solution I'm new to differential equations, so please excuse me if I make any amateurish mistakes. -kx = mv*dv/dx After integrating: -kx2/2 + c = mv2/2 v2 = -kx2 + c This is the part I'm unsure about, the inital values: v2(0) = 0 + c = v02 So c = v02 v = (v02 - kx2/m)1/2 dx/v(x) = dt After integrating: (a bit messy) t = (m/k)1/2*arcsin(x*(k/v02m)1/2) + c c=0 Just wanted to know if I went wrong somewhere as I'm not convinced by the final answer.