Oscillations due to restoring torque

AI Thread Summary
The discussion centers on a problem involving a metal rod subjected to forces that cause vibrations in different directions. The user seeks clarification on how vibrations can occur in the x-direction when the applied force is perpendicular to that axis. It is explained that while the force causes bending in the y-direction, vibrations can still arise in the x-direction due to compression and stretching along the rod's length. The key point is to analyze the relative forces and calculate the frequency of vibrations in both directions. The user successfully interpreted the problem and found the correct answer regarding the frequency ratio.
saadhusayn
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Hi,

My problem is with A.P. French vibrations and waves question 3-10, part (b).

Question 3-10(a)

A metal rod, 0.5 m long, has a rectangular cross section of area 2 mm2. With the rod
vertical and a mass of 60kg hung from the bottom, there is an extension of 0.25 mm.
What is the Young's modulus ( N/m2) for the material of the rod?

I correctly found the Young modulus.

Part(b) asks:

(b) The rod is firmly clamped at the bottom, and at the top a force F is applied in the y direction [perpendicular to side a, parallel to side b]. The result is a static deflection, y, given by:

y=(4L^3/Yab^3)F

If the force is removed and a mass m, which is much greater than the mass of the rod, is attached to the top end of the rod, what is the ratio of the frequencies of vibration in the y and x directions (i.e., parallel to edges of length b and a)?

Here is a picture of the situation:

https://books.google.com.bd/books?i...as a rectangular cross sectional area&f=false

I don't understand the situation here. If the force that bends the rod is parallel to the y axis, how do the vibrations parallel to the x-axis arise?

Thank you in advance for your help.
 
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Parallel to the x-axis it is compressing-stretching the rod along its length. Parallel to the y-axis it is bending. The question is asking you to figure out the relative forces in these two directions. Then you must work out the frequency of vibration. One expects that the rod will vibrate a lot faster parallel to its length due to compression-stretching.
 
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but the length of the rod is in the yz plane. How can there be any compression parallel to the x-axis?

I interpreted the question in the following way and ended up with the correct answer:

What is the the ratio of the frequency in the situation in which the shear force F is applied parallel to the y-axis and then released to the frequency when the force F is applied parallel to the x-axis and then the system is released?
 

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