Simple harmonic motion - vibration frequency

[Bugsy23]

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?

 

[Andrew Mason]

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:

$$F = ma = m\ddot{x} = -kx$$

The general solution is:

$$x = A_0\sin(\omega t + \phi)$$ where [itex]\omega^2 = k/m[/tex]<br /> <br /> $A_0$ 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). <br /> <br /> From that you should be able to determine $\omega$<br /> <br /> AM[/itex]