Question

A mass-spring system undergoes simple harmonic motion on a frictionless surface with amplitude 1.00 (meters) and angular frequency ω=

ω= 6.8 (rad/s).

Calculate the speed of the mass at the point where 1/6 of the total energy is kinetic energy.

Answer 1

Answer

Total energy

$E=\frac{1}{2}m\omega^2A^2$

And kinetic energy

$KE=\frac{1}{12}m\omega ^2A^2\\\frac{1}{2}mv^2=\frac{1}{12}m\omega ^2A^2\\$

$v=\frac{\omega A}{\sqrt{6}}\\v=\frac{6.8×1}{\sqrt{6}}=2.77m/s$