A 0.25 kg harmonic oscillator has a total oscillation energy of 4.0 J. If the oscillation amplitude is 20.0 cm, what is the oscillation frequency?
A) 4.5 Hz
B) 1.4 Hz
C) 2.3 Hz
D) 3.1 Hz

Question

Quizplus · Accepted Answer

The oscillation frequency is given by:$$f = \sqrt{\frac{k}{m}}$$where k is the spring constant and m is the mass. The spring constant is given by:$$k = \frac{m\omega^2}{A^2}$$where $\omega$ is the angular frequency and A is the oscillation amplitude. Substituting this into the first equation, we get:$$f = \sqrt{\frac{m\omega^2}{mA^2}} = \frac{\omega}{2\pi A}$$Substituting the given values, we get:$$f = \frac{\sqrt{4.0 J/(0.25 kg)}}{2\pi (0.20 m)} = 4.5 Hz$$

A 025 Kg Harmonic Oscillator Has a Total Oscillation Energy of of 4.0