Answer to Question #160922 in Classical Mechanics for Quanta

Question

A 50.0 g object connected to a spring with a force constant of 35.0N/m oscillates with amplitude of 4.00cm on a frictionless, horizontal surface. Find
(a) the kinetic and potential energy when its position is 3.00cm

Answer 1

$U=\frac{kx^2}{2},$

$U=\frac{35\cdot 0.03^2}{2}=15.75~\text{mJ},$

$\omega=\sqrt{\frac km},$

$cos \omega t=\frac xA,\\sin\omega t=1-\frac{x^2}{A^2},$

$K=\frac{m\omega^2A^2sin^2\omega t}{2}=\frac{k(A^2-x^2)}{2},$

$K=\frac{35\cdot(0.04^2-0.03^2)}{2}=12.25~\text{mJ}.$