# Pendulum frequency

1. Jul 17, 2010

### aletof

Hi!

I want to build a machine, but I need some precise calculations to complete it. I basically need to have various pendulums of the same length but different frequency

I was thinking on using some weights that I could set higher or lower on the pendulum to adjust the frequency.

I want to calculate the frequency given the following information:

-Length of the pendulum (will be constant)
-Weight of the material used throughout the pendulum (will be constant)
-Additional adjustable weight
-Height of the additional weight

I hope it is not to difficult to come up with a formula that considers all of this.

Thanks in advance!

2. Jul 17, 2010

### Staff: Mentor

3. Jul 17, 2010

### aletof

Thanks, I was reading this article: http://en.wikipedia.org/wiki/Center_of_percussion
which describes somewhat my problem, unfortunately I haven't been able to deduce a formula that would enable me to precisely calculate the real (I'm actually going to build it) frequency of a pendulum, given the above described criteria.

I reckon I need something like this:

http://www.wolframalpha.com/input/?...scillations.I-.*PendulumSmallOscillations.m--

Looking at the schematic I want to keep the length static, and move the red ball up and down along the black line (it will be rigid, not a string), thus modifying the period/frequency.

4. Jul 17, 2010

### Staff: Mentor

You'll want to treat it as a physical pendulum. See: http://hyperphysics.phy-astr.gsu.edu/Hbase/pendp.html" [Broken].

You'll need to calculate the rotational inertia about the pivot and the distance of the center of mass from the pivot.

Last edited by a moderator: May 4, 2017
5. Jul 17, 2010

### aletof

What I understand is that this is the formula that's going to help me:

Where:
-"m" is the total mass of my pendulum
-"g" is gravity
-"L" is the length from the pivot to the end of the pendulum
-"Isupport" is the moment of Inertia which I have to calculate with:

Where:
-"r" is the distance from the pivot to the center of mass?

I'm not sure if I'm interpreting things correctly on this one, I need to perform the calculation for about 20 different pendulums, so deducing a formula where I can input my data and get the result is my priority.

Now, it troubles me that this will work only for "small displacements", what exactly is a small displacement on this case?

Thanks for your help so far!

6. Jul 17, 2010

### Staff: Mentor

Depending on how you are distributing the mass along the pendulum, you can simplify the calculations for the center of mass and rotational inertia.

The link I gave describes where the 'small angle' approximation comes in. You can always extend it to greater accuracy, if you like.

7. Jul 17, 2010

### aletof

The pendulum will be a straight wooden stick and the weight will be a lead or steel piece that I can move along the length of the stick, thus changing the center of mass.

Ideally all the pendulums will have the same weight, but just by offsetting the steel weight I will be able to change the frequency significantly.

I guess I need to figure out how to calculate the center of mass, based on the position and mass of the steel weight as well as the rotational inertia, I could then input those on the above mentioned formula and it should work?

8. Jul 17, 2010

### Staff: Mentor

If you can neglect the weight of the stick compared to the steel weight, you can treat it as a simple pendulum. Otherwise, you'll need to treat it as a physical pendulum as we've been discussing.

I suspect you'll be fine by approximating the steel weight as a point mass. Then you can easily calculate the combined center of mass and combined rotational inertia. The rotational inertia of a point mass is mr²; that of a stick rotating about one end is 1/3mL². (All of this can be found on the hyperphysics site.)

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