Lightly Damped Simple Harmonic Oscillator

[DrDank]

Tuning forks are lightly damped SHO's. Consider a tuning fork who's natural frequency is f=392Hz. Angular frequency = w = 2(Pi)f = 2463 (rad/s)

The damping of this tuning fork is such that, after 10 sec, it's amplitude is 10% of it's original amplitude.

Here is my attempt to find the damping factor (gamma)
Amplitude as a function of time where g is the damping factor (g = gamma)$$A(t) = A_{o} e^{-t\gamma}$$

$$A(10) = \frac{1}{10} A(0)$$

$$A_{o}e^{-10\gamma} = \frac{1}{10} A_{o} e^{0}$$

$$e^{-10\gamma} = \frac{1}{10}$$

$$-10 \gamma = \ln{\frac{1}{10}}$$

$$\gamma = \frac{\ln{10}}{10} = .23$$

Is this right?

 

[jtbell]

You can check your result yourself by substituting it back into the original equation.