A 0.25 kg harmonic oscillator has a total mechanical energy of 4.1J. If the oscillation amplitude is 20.0 cm. What is the oscillation frequency?
A)4.6 Hz
B)1.4 Hz
C)2.3 Hz
D)3.2 Hz

Question

A 0.25 kg harmonic oscillator has a total mechanical energy of 4.1J. If the oscillation amplitude is 20.0 cm.  What is the oscillation frequency?
A)4.6 Hz
B)1.4 Hz
C)2.3 Hz
D)3.2 Hz

Quizplus · Accepted Answer

The oscillation frequency is given by:$$f = \frac{1}{2\pi} \sqrt{\frac{k}{m}}$$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:$$f = \frac{1}{2\pi} \sqrt{\frac{m\omega^2}{mA^2}}$$$$f = \frac{\omega}{2\pi A}$$The angular frequency is given by:$$\omega = \sqrt{\frac{k}{m}}$$Substituting this into the previous equation, we get:$$f = \frac{1}{2\pi A} \sqrt{\frac{k}{m}}$$$$f = \frac{1}{2\pi A} \sqrt{\frac{4.1 J}{0.25 kg}}$$$$f = \frac{1}{2\pi (0.2 m)} \sqrt{\frac{4.1 J}{0.25 kg}}$$$$f = 4.6 Hz$$

A 025 Kg Harmonic Oscillator Has a Total Mechanical Energy of of 4.1J