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

[pitbull]

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?

Homework Equations

...

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?

 

[haruspex]

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.

 

[gneill]

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

 

[pitbull]

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.

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?

 

[gneill]

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.