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## Homework Statement

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).

## Homework Equations

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)

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!