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DrDank
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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)[tex]A(t) = A_{o} e^{-t\gamma} [/tex]
[tex]A(10) = \frac{1}{10} A(0) [/tex]
[tex]A_{o}e^{-10\gamma} = \frac{1}{10} A_{o} e^{0}[/tex]
[tex]e^{-10\gamma} = \frac{1}{10} [/tex]
[tex]-10 \gamma = \ln{\frac{1}{10}} [/tex]
[tex]\gamma = \frac{\ln{10}}{10} = .23[/tex]
Is this right?
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)[tex]A(t) = A_{o} e^{-t\gamma} [/tex]
[tex]A(10) = \frac{1}{10} A(0) [/tex]
[tex]A_{o}e^{-10\gamma} = \frac{1}{10} A_{o} e^{0}[/tex]
[tex]e^{-10\gamma} = \frac{1}{10} [/tex]
[tex]-10 \gamma = \ln{\frac{1}{10}} [/tex]
[tex]\gamma = \frac{\ln{10}}{10} = .23[/tex]
Is this right?
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