1. The problem statement, all variables and given/known data A mass m is sliding back and forth in a simple harmonic motion (SHM) with an amplitude A on a horizontal frictionless surface. At a point a distance L away from equilibrium, the speed of the plate is vL (vL is larger than zero). 2. Relevant equations What is the period of the SHM? 3. The attempt at a solution a_x=-kx/m -> vX= (-kx^2)/(2m) k = (-vX*2m)/(x^2) T=2π*√(m/k)=2π*√(m/((-vX*2m)/(x^2)) T=2π√((-x^2)/vX)) Filling in point at distance L from equilibrium, I get: T=2π√((-L^2)/vL)) The correct answer is T=2π√((A^2-L^2)/vL)), but I cannot imagine where the A^2 comes from. Any help is appreciated!