SHM of a Tuning Fork: Calculating Maximum Velocity and Acceleration

AI Thread Summary
The discussion centers on calculating the maximum velocity and acceleration of a tuning fork's prong in simple harmonic motion (SHM). The prong's movement is described with an extreme position distance of 2.29 mm, leading to confusion about the correct amplitude, which should be half of this distance. Initial calculations for maximum velocity and acceleration were incorrect due to unit errors and misunderstanding of amplitude. After clarification, the correct amplitude is established, leading to revised calculations of maximum velocity at 6.33 m/s and maximum acceleration at 17518 m/s². The importance of accurately determining amplitude in SHM calculations is emphasized.
shorti2406
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Q: 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 2.29 mm. If the frequency of the tuning fork is 440.2 Hz, what are the maximum velocity and the maximum acceleration of the prong? Assume SHM.


I was just hoping somebody could tell me if I did this problem correctly :smile:

For Vmax I have : (2л) x (440.2Hz) x (0.0029cm) = 8.02 m/s

For amax I have : [(2л x 440.2Hz)^2] x (0.0029cm) = 22185 m/s2


I would appreciate any input! Thanks!
 
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shorti2406 said:
Q: 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 2.29 mm. If the frequency of the tuning fork is 440.2 Hz, what are the maximum velocity and the maximum acceleration of the prong? Assume SHM.


I was just hoping somebody could tell me if I did this problem correctly :smile:

For Vmax I have : (2л) x (440.2Hz) x (0.0029cm) = 8.02 m/s

For amax I have : [(2л x 440.2Hz)^2] x (0.0029cm) = 22185 m/s2


I would appreciate any input! Thanks!

Not quite- What is the amplitude of the motion?

Plus- you will need to be a lot more careful with the units
 
Last edited:
Oh, okay... so then:

Vmax : (2л) x (440.2Hz) x (0.00229m) = 6.33 m/s

amax : [(2л x 440.2Hz)^2] x (0.00229m) = 17518 m/s2

Does that look about right? Or am I still way off?
 
The amplitude is still not correct.
 
Well, I think I'm just stuck then. Can anybody give me a clue as to what the correct amplitude shoudl be? I would really appreciate it!
 
shorti2406 said:
Well, I think I'm just stuck then. Can anybody give me a clue as to what the correct amplitude shoudl be? I would really appreciate it!
You'll smack yourself in the head when you realize it:
The distance the prong moves between its extreme positions is 2.29 mm.

Remember that amplitude is the maximum displacement from the equilibrium position, not the distance between the extreme positions.
 
You're right. I have no idea why I didn't realize that! Thank you so much for you help.
 

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