Construction of a Foucault Pendulum

  
       
  During my Dynamics course at NMSU, our professor put forth the challenge that anyone constructing a Foucault Pendulum would receive extra credit.  I couldn't pass up the challenge!  Actually, the single most difficult part, was finding a suitable location with a high enough and stable ceiling to suspend the pendulum.  I considered a hundred different options, but ultimately, it was much less hassle to just work at home.  
       
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  Pendulum bob.  Constructed of 4” PVC end caps, support hole center-drilled by lathe, filled with 14 lbs lead shot, and coupled by section of PVC pipe.    
       
   
 

I do have the benefit of a lathe to make items such as this ferrule.  From what I read, I needed a nice smooth bell or parabolic shape to allow the suspension wire to swing without creating stress.  Unfortunately, I began the design for a wire suspension for strength, but soon realized there was far too much energy loss.  String was not a good choice, but the obvious choice was a high strength fishing line which worked perfectly.

 Since I ultimately suspended the pendulum at home, the absolute highest location was a skylight in the entryway.  That gave me 13', which is a bit short, but still worked.  To keep the equations of motion as linear as possible, the pendulum swing arc was limited to only a few inches.  This picture shows the apparatus to hold the ferrule with string in the skylight.  The container depicting the string merely shows the string hanging in the vertical, which does not ideally account for proper perspective.  
       
       
   
 

The calculations indicate the pendulum should rotate approximately nine degrees clockwise due to the earth's rotation.  This nine degrees is depicted by taut strings measured out by the protractor.

 The only way to get a true initial swing is to tie the pendulum bob out of the vertical with a string, let all perturbations subside, and then use a lighter to burn the string, thereby initiating the first swing.  Even then, if this "displacement string" is not attached at the proper point on the bob, the bob will still undergo oscillations.  
       
       
   
 

I used a timelapse camera to record the action and assemble into video.  This is the initial picture with the timelapse camera actually aligned for the final position.  As a result, it is difficult to see the initial alignment in this picture.  If the camera was moved right, then it would be clear the pendulum bob was in fact lined up with the leftmost mark.

 Since the camera was in fact lined up for the final result, here you can see after one hour, this frame does indeed show the pendulum has indicated the earth's rotation through nine degrees, which is the rightmost mark.  
       
       
   
 

Even though the results were demonstrated, the camera arrangement makes it difficult to both visualize and verify the results.  This is abundantly seen in the above picture where the viewer simply has to accept the pendulum is lined up with the starting mark since it cannot be seen without a different camera angle.  To overcome this limitation, I decided to set a camera up directly under the pendulum and record the path of an illuminated LED.

 I fabricated an enclosure for the LED to ensure just a single point of light to depict the path.  All of the battery powered wiring is contained within the bob.  
       
       
 

 
 

This is the final configuration with the camera staring up with a wide angle lens, directly under the pendulum bob and LED.

 Here is the time exposure test of a swing with a clock to show the proper passage of time.  A sheet of plexiglass was placed above the camera and below the pendulum.  This gave a place to set the clock and also save the camera in case the pendulum apparatus broke free.  
       
 

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This is the final composite of the LED path, showing the earth's rotation of approximately nine degrees in one hour, or in this case, the results were closer to ten degrees.  The final swing also shows the nutation inevitable with a non-ideal set up.