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A Double Pendulum Gravimeter

First created: Sat Jun 2 2001
Last Updated: Sun Jul 15 2001
 
To observe the gravitational tidal pull of the Moon and the Sun using a simple home built device, I propose to use a pair of rigid coupled pendulums. The top one, hinged from above is a direct pendulum. The bottom one, hinged from below, is an inverted pendulum. The two are coupled in a way that the instability of the bottom pendulum is compensated by the stability of the top one. The device is extremely sensitive to horizontal forces.

This sensitivity can be used to detect the horizontal components of the tidal pull of the Moon and the Sun. These components are smallest for a body, Moon or Sun, on the horizon or at the vertical, and reach a maximum when the body is around 45 degrees above or below the horizon.

Developing The Model

A mathematical model of the device and its physics looks promising. Tidal forces could produce deflections as large as 1/10 th of a millimeter. I also looked at some other topics related to this design.

Building The Device

An outline sketch of the device is shown on the left. It consists of a pair of glass strip pendulums coupled through small magnets. I am also preparing a more detailed description.

The frontend detector uses a paper flag attached to the top pendulum and oscillating between a bright diode and a phototransistor. This displacement measurement technique is the same used in by the magnetic gravimeter.

The frontend signal is then amplified and plotted. The circuits used are again similar to that of the magnetic gravimeter, minus the feedback circuit. At this time I am recording without any amplification.

Temperature compensation is also needed. At this time I have only temperature monitoring in place, but no control feedback.

Once temperature control is in place the frontend signal can be amplified and still remain within the range of the position detector. That's something I still have to do.

Experimental Results

My best results to date include a 5 day sequence around the 4th of July, 2001; the house was empty and the air conditioning turned off, so conditions were ideally stable. For these dates the Fourier transform shows peaks at 24 hours and 12 hours. The 12 hour peak does not appear to be temperature related. Could this be the tidal signal?

The latest results include temperature monitoring, but not control. The pendulum displacement measured is raw, not amplified. The temperature measurement is only amplified 10 times (not 100).