Velocity of a mass m that moves along the x-axis

[lily]

Homework Statement

A particle of constant mass m moves along the x-axis. Its velocity v and position x satisfy the equation: 1/2m(v^2 - v0^2) = 1/2k(x0^2-x^2), where k, v0 and x0 are constants. Show that whenever v does not equal 0, mdv/dt=-kx.

Relevant Equations

1/2m(v^2 - v0^2) = 1/2k(x0^2-x^2)

mdv/dt=-kx.

dv/dt(mv^2-mv0^2) = dv/dt(kx0^2-kx^2)

 

[anuttarasammyak]

Relevant Equations:: 1/2m(v^2 - v0^2) = 1/2k(x0^2-x^2)

Differentiate the both hand sides by time i.e. d/dt