Penduleum Payloads and SpeedJacob KaginAward: Top 100
School: vacaville christian school By tying two expo markers to a pendulum at various lengths we can determine the full period of the pendulum itself. Using these marks, we can identify a few key insights about the nature of pendulums. Mainly, despite the fact that the marks are different in length, the time it took to create them remained exactly the same. We can actually derive the pendulum period equation, and using our known values, to determine that the actual speed of the markers changes depending on how far up the pendulum they are placed. Where the marker closer to the edge of the pendulum moves faster than the one closer to the origin. This can be further described with energy. Since the the law of conservation of energy determines that the energy of a closed system must always be conserved (We are assuming that pendulum is a closed system and negligible energy is lost due to heat and friction), We can determine the difference in velocity simply by observing the marker's potential energy due to gravity. Since the change in potential energy is due to how high the amplitude is from the marker's equilibrium point. Since the marker closer to the original (Marker one) has a smaller arc compared to that of marker two (the marker closer to the weight) the maximum potential energy of marker one is less than that of two. Now applying the energy law, we can then determine that the maximum kinetic energy of marker one is also less than two's. Due to kinetic energy being: ½ mv^2, and assuming the masses of the markers are the same, we can determine that the velocity component of marker one must be smaller than the component of marker two. The relationship is interesting as it shows how even small changes in a single mechanical device can drastically impact its nature, and goes on to show how, with physics, just knowing a few values of a system can determine almost all aspects of it. 
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