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| Here’s the data about our pendulum: • 10 pound weight used as pendulum bob • support string/rod 87″ • diameter of the pendulum bob 10″ • 4 feet launch height |
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| Pendulums don’t normally come to mind these days. A short story by Edgar Allen Poe read when I was a child called “The Pit and the Pendulum,” was the stuff of nightmares for an entire winter. I am still uncertain if it was the inexorable action of the device or the fact that the Catholic Church actually sanctioned its use as a method of torture that creeped me out more.
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Apart from the stuff of nightmares, the pendulum was used in time-keeping for hundreds of years.
 Then there is a permutation of the pendulum in Newton’s Cradle: Outside of the zillions of $ that someone made with this show and the desktop toy, the pendulum seems kind of useless today; timekeeping functions (and torture devices!) have all been superseded by silicon. The machine age dies hard. Long live the electronic age! Just like everything else that looks simple, the math relating to the pendulum is complicated. |
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| A few items came up while researching this topic that I found interesting: • Gravitational Potential Energy is defined as the product of Mass*Gravity*Height. • Gravity is measured as the gravitational acceleration of an object near the surface of the Earth at 9.80665 m/s2 • Kinetic energy increases in direct proportion to the increase in mass and with the square of the increase in velocity. • Graphed/plotted the action of the pendulum looks like a sine wave • Given a fixed (unmoving) length, each pendulum possesses a single resonant frequency |
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For some inexplicable reason, I obsessed on solving for the angle of our rod/string once the bob was pulled out at four feet. I don’t know if this is correct, but this is what I am thinking:Using the data for the pendulum created in class the string (rod) measured 87″ and the diameter of massy-bob was ten inches. Literature suggests that the length of the rod be measured from the point of frictionless attachment to the center of the bob (87″ + 5″ = 92″= L). |
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| We set the bob in motion from a height of 48″ which is shown in line AC. Point A-B is defined as AC – the height or 92 – 48 or 44″  |
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| Given side AC = 92″ and side A-B = 44″ Pythagorean theorem: A (squared)+ B (squared) = C (squared) (X) + 44(44) = 92(92) then (x) + 1936 = 8464 then (x) = 8464-1936 or (x)= 6528 (x) = square root of 6528 = 80.79″ Which means we now have the bottom leg of the triangle (BC) measured at 80.79″ or 81″. |
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| arccos= Hypotenuse/adjacent = arccos=92/44 = Theta = 61 degrees. | |
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| With little thanks to troubled years, I have earned a respectful appreciation and antipathy toward pendulum action: | |
| Berta, Branford Marsalis • August Wilson, The Piano • YouTube link
Peter Terezakis |
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