# Oscillations due to restoring torque

In summary, the conversation discusses a problem with A.P. French vibrations and waves, specifically question 3-10 part (b). The question deals with a metal rod that is clamped at the bottom and has a force applied at the top in the y direction. It asks for the ratio of frequencies of vibration in the y and x directions when a mass is attached to the top end of the rod. The conversation also includes a picture and a clarification of the situation. The summary concludes with a mention of how the question was interpreted and the correct answer was found.
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.

(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?

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.

poseidon721
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?

## 1. What is the definition of "Oscillations due to restoring torque"?

Oscillations due to restoring torque refer to the repetitive back and forth motion of a system caused by a restoring torque, which is a force that acts to return the system to its equilibrium position after being displaced.

## 2. How do oscillations due to restoring torque occur?

Oscillations due to restoring torque occur when a system is disturbed from its equilibrium position and experiences a restoring force that acts to return it to that position. This results in repetitive motion around the equilibrium point.

## 3. What are some examples of oscillations due to restoring torque?

Some examples of oscillations due to restoring torque include a pendulum, a mass on a spring, a simple harmonic oscillator, and a swinging door. These systems all experience a restoring torque that causes them to oscillate back and forth.

## 4. How is the period of oscillations due to restoring torque determined?

The period of oscillations due to restoring torque is determined by the mass of the system, the strength of the restoring torque, and the initial displacement. It is also affected by external factors such as friction and air resistance.

## 5. What is the relationship between amplitude and frequency in oscillations due to restoring torque?

The amplitude and frequency of oscillations due to restoring torque are inversely proportional. This means that as the amplitude increases, the frequency decreases, and vice versa. This relationship can be described by the equation T = 2π√(m/k), where T is the period, m is the mass, and k is the spring constant.

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