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. Please help!!!

Answer 1

something is wrong with your formula, since the units do not match up.
1/2 m (2v) dv/dt = 1/2 k (-2x) dx/dt
mv dv/dt = -kx dx/dt
Am I missing something here?