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).
What is the period of the SHM?
The Attempt at a Solution
a_x=-kx/m -> vX= (-kx^2)/(2m)
k = (-vX*2m)/(x^2)
Filling in point at distance L from equilibrium, I get:
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!