Friction in a simple mathematical pendulum

[MathematicalPhysicist]

How do I guarantee that that the friction in the movement of a simple mathematical pendulum is negligible?

 

[BvU]

Use a heavy weight, minimize air resistance, use diamonds for bearings, etc...

 

[MathematicalPhysicist]

Use a heavy weight, minimize air resistance, use diamonds for bearings, etc...

Heavy weight compared to the stand that the pendulum is situated on it, or something else?

 

[BvU]

Heavy weight compared to

the air that has to be pushed aside for the pendulum to move. Can also be achieved by putting the whole thing in vacuo.

friction in the movement of a simple mathematical pendulum is negligible?

To what purpose ? Saving energy, building a pepertuum mobile, verifying $T=2\pi \sqrt{g\over l}$, other ?

Familiar with the Reversible (Kater's) Pendulum ?

 

[MathematicalPhysicist]

the air that has to be pushed aside for the pendulum to move. Can also be achieved by putting the whole thing in vacuo.

To what purpose ? Saving energy, building a pepertuum mobile, verifying $T=2\pi \sqrt{g\over l}$, other ?

Familiar with the Reversible (Kater's) Pendulum ?

Verifying the formula.

 

[MathematicalPhysicist]

The link you gave is for the physical pendulum, I referred to the mathematical point mass pendulum.

I should have said that it's point mass.

 

[BvU]

There's a good expression for $T$ with damping, so you can measure the damping by following the amplitude as a function of time (all pendula have damping) and correct $T$. Depending on the accuracy of your measurements (in particular: L!), you can allow quite a bit of damping before such a correction becomes the main source of inaccuracy.

 

[BvU]

it's point mass

Do they exist ? What are you doing to verify this T formula ?

 

[BvU]

link you gave is for the physical pendulum

Nice thing about that one is that it is the exact equivalent of a mathematical pendulum.

 

[BvU]

Don't see no point mass ...
So you want to ask yourself:

With what accuracy can I measure L and T
Do I need to correct for damping ? How much damping is there ?
What is the correction to T for the fact that this is a ball and not a point mass ?

 

[DrClaude]

Don't see no point mass ...

The post has been removed because it contained a picture in which some personal information could be seen.

 

[BvU]

Only looked at the picture when it was still there.

Way I meant it was that a $\ \ \approx$ 1 inch diameter metal ball is not a point mass.

 

[MathematicalPhysicist]

Only looked at the picture when it was still there.

Way I meant it was that a $\ \ \approx$ 1 inch diameter metal ball is not a point mass.

So I guess it should work as a mathematical pendulum when the angle of release of the ball is small.

How do I find the limits of small angles appropriate for a suitable mass?

 

[BvU]

How do I find the limits of small angles appropriate for a suitable mass

Experiment !

[edit] and of course, nowadays you also use your big brother friend google for a peek at the expression ... $\qquad$

 

[MathematicalPhysicist]

@BvU but can't I know from theory what to check for?

 

[BvU]

was one step ahead of you see #14

 

[MathematicalPhysicist]

Experiment !

[edit] and of course, nowadays you also use your big brother friend google for a peek at the expression ... $\qquad$

Good to know there's big brother.

I feel like there's no more need to work, everything is in the net nowadays :-D

 

[BvU]

Yes, why bother trying to determine $g$ when you can also look it up

 

[WhatIsGravity]

Here’s a link to the patent for the most accurate pendulum yet created; quite a feat of engineering.
http://www.freepatentsonline.com/y2015/0234087.html

 

[BvU]

Picture when still there showed a 1" steel ball hanging from two nylon wires attached to a rod. Pendulum length will already be difficult to measure accurately.

 

[jrmichler]

The patent application linked in post #19 issued as Patent #9,291,742 in 2016. It's assigned to Micro-g LaCoste, Inc. (http://microglacoste.com), a company that makes gravimeters. They make a portable model that measures gravity with an accuracy of better than 10 micro gals (1E-8 G). They have over a dozen patents on gravity meters.

 

[gmax137]

Someone linked a paper here a few years back, that gave expressions for a dozen or more corrections to the simple formula. They accounted for the non-small angle, the mass of the string, and a bunch more that I don't recall. I can't find it right now but a good search should turn it up.