Prong Set
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What's the Maximum Acceleration of the Prong?
The prong of a tuning fork moves back and forth when it is set into vibration. The distance the prong moves between its extreme positions is 2.25 mm. If the frequency of the tuning fork is 440.3 Hz, what are the maximum velocity and the maximum acceleration of the prong? Assume SHM.
What's the maximum acceleration? I tried different formulas, but I still didn't get an answer. Please help!
You're probably familiar with the formula
T=2pi*rad(L/g) ...looks more familiar with the actual rad and pi symbol.
T is the time it takes to complete one period. g is the acceleration due to gravity, which is at maximum when the mass is at its extremes. In our case, the maximum acceleration is also at the extremes -- there we can replace g with a (acceleration).
We then can solve T=2pi*rad(L/a), given that we have T and L (length).
We are given length L = 0.0025m. Given f = 440.3 Hz (cycles per second), the period T is 1/440.3 = 0.0022712 seconds.
--
Plugging into T=2pi*rad(L/a):
0.0022712 s = 2pi*rad(0.0025m /a)
a = 19132.3114 m/s^2
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