Simple Harmonic Motion Tuning Fork Question

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Homework Help Overview

The discussion revolves around a problem related to simple harmonic motion, specifically involving a tuning fork vibrating at a frequency of 264 Hz and the movement of its prongs. The original poster seeks to calculate the maximum speed of the tip of a prong, given the amplitude of movement.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to use the formula Vmax = omega*A but expresses uncertainty about how to determine the amplitude (A). Some participants clarify that the amplitude is the distance the prong moves from the center, which is 1.66 mm. The poster later revisits the formula and considers the relationship between frequency and period to express Vmax.

Discussion Status

The discussion is ongoing, with participants providing clarifications and suggestions. The original poster acknowledges a mistake in their calculations but does not indicate a resolution to the problem. There is an exploration of the relationships between variables involved in the motion.

Contextual Notes

The original poster mentions converting units from mm to m, indicating attention to detail in the calculations. There is an implicit assumption that the problem requires understanding of harmonic motion principles and the relationships between frequency, amplitude, and maximum speed.

ninjagowoowoo
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Q:
A tuning fork vibrates at a frequency of 264 Hz and the tip of each prong moves 1.66 mm to either side of center. Calculate the maximum speed of the tip of a prong.

So far I've found that Vmax = omega*A, but I don't know how to find A. Am I going in the wrong direction? Or is there a way to find A that I don't know about yet..?
 
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ninjagowoowoo said:
... the tip of each prong moves 1.66 mm to either side of center.
That's the amplitude.
 
Oh haha, I knew it must've been something stupid, thanks.
 
Ok so I figured that Vmax would be omega*A, but it isn't correct. I know that
v=-omega*A*sin(omega*t) (yeah I need to learn how to write equations better)

so I assumed that in the problem, it's basically an initial value, so t=0. So that would leave v=omega*A.

From this I got Vmax = (2pi/T)(A)
and T=1/f

so Vmax = (2pi/(1/f))(A)

I guess this is incorrect. Oh and I didnt forget to convert mm to m. Any pointers?
Thanks
 
woops nevermind... I must have entered it in my calculator wrong haha sorry. Thanks for the help Al.
 

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