# DU/dt = 0 for oscillating spring, help with derivation

by docholliday
Tags: springs mechanics
 P: 5 U = energy In the book: $\frac{dU}{dt} = \frac{d}{dt} (\frac{1}{2} mv^2 + \frac{1}{2} kx^2)$ then we have $m \frac{d^{2}x}{dt^2} + kx = 0$ because $v = \frac{dx}{dt}$ however they get rid of $\frac{dx}{dt}$ . They are ignoring the case where v = 0, because then $m \frac{d^{2}x}{dt^2} + kx$ doesn't have to be zero, and it can still satisfy the equation.