# Foucault pendulum: diagnosing experimental systematics

I did the Foucault pendulum experiment today. I used a 45 pound weight hung on about 12 or 15 feet of inelastic cord. I understand that a great and highly precise experiment will show one full rotation of the plane of oscillation in about 24 hours, but my pendulum was rotating at a rate that appears to be too fast.

Here is a gif of the experiment showing the precession in the counterclockwise direction.

What would be the causes of too fast rotation? The Earth's rotation must impart a torque on the weight through the twisting of the cord, can that increase rotation speed? Here is my main question: can I trust the underlying signal of the counterclockwise rotation even though it is going too fast? Is this experiment sufficient to show that I am in the southern hemisphere? What might cause the too fast rotation? I released the pendulum by burning its restraint cord, and you can see the initial motion is very nearly planar with little to no elliptical deviation. How can I improve my experiment? I will get some metal wire today and replace the nylon cord with metal wire for a repeat experiment. Please criticize my experiment to help me diagnose the systematics which lead to the too fast rotation. The time elapsed in the gif is about 6 minutes.

• I think your cord is too short.
– Eli
Nov 23, 2020 at 15:48
• What effect doyou believe to be caused by the shortness of the cord? Nov 23, 2020 at 16:27
• The vertical motion must be small, In Munich is the cord length 60m
– Eli
Nov 23, 2020 at 16:40
• Thank you. Why must the vertical motion be small? Nov 23, 2020 at 16:41
• Because you need plane motion, to see the effect of the earth rotation
– Eli
Nov 23, 2020 at 18:05

A Foucault pendulum setup is very finicky.

A properly constructed Foucault pendulum setup can show the Earth's rotation because the effect of the Earth's rotation on the orientation of the plane of swing is cumulative. This strength is also a weakness; the effect from any bias in the setup also accumulates.

A common source of deviation from the idealized case is when the wire is not equally bendable in all orientations.

Assume the simplest case of an uneven wire. Let me call the direction of least stiffness the x-direction and the direction of most stiffness the y-direction. Let the pendulum start swinging in an orientation that is in between the x-direction and y-direction.

The stiffness of the wire gives rise to an additional restoring force. The effect is very small, but the Foucault pendulum setup is so sensitive that even very very small effects can cause significant deviation from the idealized case.

The plane of swing will then tend to open up. The plane of swing opening up introduces additional deviation.

For most cases: to an acceptable approximation when the amplitude of swing is small the period is independent of the amplitude. But a Foucault pendulum setup is so senstive that the difference does matter.

So, with the plane of swing opened up the motion of the pendulum bob is along an elongated ellipse. Motion along the perimeter of an ellipse can be thought of as a superposition of two perpendicular oscillations. with the plane of swing opened up you get that superposition, and the two constituting oscillations don't have exactly the same period. The difference is very small, but the consequences of that difference accumulate.