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Simple harmonic motion - vibration frequency

by Bugsy23
Tags: frequency, harmonic, motion, simple, vibration
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Bugsy23
#1
Oct18-10, 10:57 AM
P: 25
I need to calculate the frequency of sinusoidal vibrations in simple harmonic motion. The only known values that I have are the acceleration amplitude and the vibration amplitude. Is there a way of calculating the frequency of vibration without knowing the period of the oscillations?
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Andrew Mason
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Oct18-10, 12:12 PM
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Quote Quote by Bugsy23 View Post
I need to calculate the frequency of sinusoidal vibrations in simple harmonic motion. The only known values that I have are the acceleration amplitude and the vibration amplitude. Is there a way of calculating the frequency of vibration without knowing the period of the oscillations?
The equation of motion is:

[tex]F = ma = m\ddot{x} = -kx[/tex]

The general solution is:

[tex]x = A_0\sin(\omega t + \phi)[/tex] where [itex]\omega^2 = k/m[/tex]

[itex]A_0[/itex] is the maximum amplitude of vibration (maximum x). The maximum acceleration occurs when x = ? What is the acceleration at that point? (hint: use the equation of motion to find maximum value for a).

From that you should be able to determine [itex]\omega[/itex]

AM


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