A harmonic oscillator starts with an amplitude of 20.0 cm. After 10.0 s, the amplitude decreases to 15.0 cm. If the linear damping coefficient is 2.00 Ns/m, how much mass is oscillating?
A)30.0 kg
B)15.0 kg
C)34.8 kg
D)17.9 kg
E)3.88 kg

Question

Quizplus · Accepted Answer

The damping coefficient is given by:$$b=2m\beta$$where m is the mass and \beta is the damping constant. The damping constant is given by:$$\beta=\frac{1}{2\pi}\ln\left(\frac{A_0}{A}ight)$$where A_0 is the initial amplitude and A is the amplitude after time t. Substituting these equations into the first equation, we get:$$b=m\ln\left(\frac{A_0}{A}ight)$$Solving for m, we get:$$m=\frac{b}{\ln\left(\frac{A_0}{A}ight)}$$Substituting the given values, we get:$$m=\frac{2.00	ext{ Ns/m}}{\ln\left(\frac{20.0	ext{ cm}}{15.0	ext{ cm}}ight)}=34.8	ext{ kg}$$

A Harmonic Oscillator Starts with an Amplitude of 20