# Optimizing the Pivot Point for a Uniform Bar's Frequency of Oscillation

• pitbull
In summary, the conversation discusses a problem involving finding the optimal point to hang a uniform bar for maximum frequency of small oscillations. The suggested approaches include using the physical pendulum formula and applying the Lagrange method.
pitbull
Gold Member

## Homework Statement

Given a uniform bar of length L, which point should you hang it from (between 0 and L) so that you get maximum frequency for small oscillations?

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## The Attempt at a Solution

It seems like a basic problem, but I don´t know how to start. Could you guys give me some clues to start it?

pitbull said:
It seems like a basic problem, but I don´t know how to start. Could you guys give me some clues to start it?
First, draw a diagram of the bar in some position and find the forces on it. If you can't post diagrams readably then describe it as well as you can.

pitbull
Look up "physical pendulum" and refresh your memory about rotational motion, moments of inertia, and so on.

pitbull
haruspex said:
First, draw a diagram of the bar in some position and find the forces on it. If you can't post diagrams readably then describe it as well as you can.

gneill said:
Look up "physical pendulum" and refresh your memory about rotational motion, moments of inertia, and so on.

Would it be easy to solve it using Lagrange method?

pitbull said:
Would it be easy to solve it using Lagrange method?
I'll admit that I haven't thought about that. I suppose that you could write the Lagrangian for the system and work from there. Give it a go and see where it takes you.

Personally I see it as a physical pendulum problem for which a formula for the period is well known. All you need to do is account for different pivot locations (a well known theorem related moments of inertia is involved) and seek a minimum.

## 1. What is the purpose of hanging a uniform bar?

The purpose of hanging a uniform bar is to demonstrate the principles of static equilibrium and the concept of center of mass. It also allows for the measurement of forces and moments acting on the bar.

## 2. How do you hang a uniform bar?

To hang a uniform bar, you will need to suspend it from a fixed point using a string or rope. Make sure the bar is level and secure before proceeding with any experiments or measurements.

## 3. What equipment do you need to hang a uniform bar?

You will need a uniform bar, a string or rope, a fixed point to hang the bar from, and a ruler or measuring device. Optional equipment may include weights and a protractor for more advanced experiments.

## 4. What factors can affect the hanging of a uniform bar?

The factors that can affect the hanging of a uniform bar include the weight and length of the bar, the angle at which it is suspended, and the location of the center of mass. External forces such as wind or vibrations can also impact the hanging of the bar.

## 5. What are some real-world applications of hanging a uniform bar?

Hanging a uniform bar can have various real-world applications, such as in construction for determining the stability of structures, in sports for analyzing the balance and stability of athletes, and in physics for understanding the principles of rotational equilibrium and center of mass.

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