Introduction: I chose to delve into this topic out of pure curiosity to see how the length of a pendulum affects its period of movement. A pendulum is a suspended point mass, hanging from a fixed point on an inextensible string. When pulled and released from one side of its equilibrium, ax°, the pendulum swings back and forth in a vertical plane under the influence of gravity (La Né Powers, 2006). The motion is periodic and oscillatory; I am determining the oscillation or otherwise known as the period of motion (Resnick & Malliday, 1977, pp. 310-311). The movement period is the amount of time it takes to swing back and forth once, measured in seconds and symbolized by T (Kurtus, 2010). Galileo discovered pendulums and discovered that the period of motion is proportional to the square root of the length - T∝√l (Morgan, 1995). Thanks to my research, I discovered that the correct method to measure the independent variable (length of the string) is from the fixed point from which it hangs (fulcrum) to the center of the mass (Cory, 2004) (Encyclopedia Britannica, 2011). The formula F=-mg sinθ shows that when a pendulum is moved from its equilibrium, it is brought back to the center restoring the force ("Pendulum", 2008). Newton's second law, F=Ma=(d^2 (Lθ))/(dt^2 ), shows that the arc through which the pendulum swings is actually a segment of a circle - the radius of which is even to the length of the pendulum. The combination of these formulas demonstrates that the mass of a pendulum is independent of its period of motion (Encyclopedia Britannica, 2011). I concluded that there is no need for a specific weight for my pendulum, although it must remain constant. As seen in the equation above, this restoring force is… the center of the paper… motion (T), measured in seconds and milliseconds. Time is recorded for five periods and averaged (T=t/5). Repeated five times for each length and average. Constant variables: the environmental conditions (indoor closed area), the weight of the pendulum, repeated the same number of times for each length, released by 10°, and the pendulum is released with the same tension into the rope every time Equipment: 6 feet of 8-strand braided nylon builder's line 0.5 ounces of 5/16-inch galvanized fender washers Scientific scales with readings from 100 to 0.01 gram A stopwatch that measures to the millisecond A clamp spring with a hole in the handle Blu-Tack 180° protractor capable assistant Stool (if necessary) Procedure: Attach the spring clamp to an object more than 160 cm tall without obstructions underneath and with the hole facing downwards.
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