# The bifilar pendulum

1. Oct 26, 2004

### almohandes

I've got an investigation in which iam investigating the factors affecting the perioad of a BIfilar pendulum. So has any one got any good ideas for me, ie: factors to be measured or kept constand, useful information that i should know, etc.

2. Oct 26, 2004

### James R

What's a bifilar pendulum?

3. Oct 26, 2004

Whatever it is, keep the swing SMALL!

4. Oct 26, 2004

### arildno

Are you talking about the DOUBLE pendulum?

5. Oct 26, 2004

### almohandes

its called bifilar, i dont know anything else

6. Oct 27, 2004

### almohandes

OK, ive decided to change the distance from the centre of the beam nad keep the rest constant, so is this right? or should i have changed the length of the string holding the aluminium baror would both ways be correct????.. but whats still confusing me is that how would i relate that factor's affect on the period using phys. principles (torque, acceleration...) and how is that factor affecting the period any way.

7. Oct 27, 2004

### James R

If you want help, you'll need to explain exactly what the thing is that you're talking about. How about a diagram, too?

8. Oct 27, 2004

### arildno

9. Oct 27, 2004

### almohandes

i've been to there but its not that much of a help

10. Oct 28, 2004

### ZapperZ

Staff Emeritus
So, was anyone else besides me is amused that the website illustrating this "bifilar" pendulum claims that this can be used to measure INERTIA!!! :)

Anyone recognize that "inertia equation"? :)

Zz.

11. Oct 29, 2004

### James R

Looks like this aims to measure the rotational inertia about the centre of mass of the test object.

I haven't checked the equation, so not sure if it is correct.

12. Oct 29, 2004

### arildno

The equation is certainly correct for measuring the moment of inertia of the object about the vertical going through the C.M.
1) Let L be the string length, D the distance between the two attached strings, W the weight of the object.
2) Rotate the object slightly in the plane.
In the following, the rotation is assumed so small that all cosines are approximated by unity.
There are two triangles two consider on each side:
a) The triangle in the vertical with the string length as the hypotenuse, and the displacement vector in the horizontal plane (normal to the direction given in that plane by the positions of the attachment points of strings in the undisplaced state).
This displacement vector has length $$L\sin\phi$$
Clearly, the component of string tension relevant for rotation in the horizontal plane, is
$$\frac{W}{2}\sin\phi$$ for a single string.
b) The triangle in the horizontal plane with D/2 as the hypotenuse; clearly we have, for the displacement vector:
$$\frac{D}{2}\sin\theta={L}\sin\phi\to\sin\phi=\frac{D}{2L}\sin\theta$$
Here, $$\theta$$ is the displacement angle in the plane.
c)Hence, the torque from one string is $$\frac{D^{2}W}{8L}\sin\theta$$
d)The angular frequency fulfills therefore the relation:
$$\omega^{2}= \frac{D^{2}W}{4LI}$$
where I is the moment of inertia of the object.
The given equation is a simple rewriting of that equation.

Last edited: Oct 29, 2004
13. May 6, 2005

### Graham

Does anyone know the equation for the period of oscilation of a bifolar pendulum oscillating in the horizontal plane? I found one involving, m, g , I, l and s but I am not sure if it is correct. I want to do an experiment to determine the moment of Inertia of the rod.