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Simple Harmonic Motion Lab Report

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Report for Experiment #13 Simple Harmonic Motion Madeline Gershman Lab Partner: Daniel Potapov TA: Rebecca Harman January 8th, 2019 Abstract This experiment studies progress of simple harmonic ... motion and dampened harmonic motion, using a system of springs to move the glider over a mostly frictionless surface. In the first investigation, the glider will simply move back and forth, supposedly without slowing down, to create a pattern of simple harmonic motion. The spring constant was found to be 2.13N/m with an uncertainty of ±0.0101. In the second investigation, the glider follows the same motion, but magnets create a dampened motion that slows the glider to a stop. The dampening coefficients of none, 2, 4, and 6 magnets, respectively are . 0597, .0845, .102, an .171.Introduction Simple harmonic motion relies on the restorative forces and follows the motion of oscillations. Newton’s second law F net=ma states that for acceleration to occur there must be a net force acting on the object. In this experiment the glider sits upon an air track and it attached to either end of the track with springs. While sitting in its equilibrium position, the glider experiences a net force of zero because each spring forces cancels the other out. When the glider is pulled from this equilibrium position, the springs with act as restorative forces and attempt to pull the glider back into this position. This spring force is represented as F s=−k ∆x where ∆ x is the displacement of the spring from its equilibrium position. With two springs, this results in an oscillating motion surrounding the equilibrium position of the glider. When there is friction or another non-conservative force in the system, this results in a dampening force. The dampening force is proportional to the velocity of the object moving, represented by F damp=−bv This results in another relationship between the amplitude of the object and the dampening force acting upon it. The amplitude decays at a constant rate of α . α= b 2m In investigation 1, simple harmonic motion is studied by determining the equilibrium position of the glider and then analyzing the amplitude, period, frequencies, and phase shift from this position as the glider is allowed to oscillate back and forth. In investigation 2, the dampening force is analyzing by increasing the force of friction acting upon the glider and observing the changes in period as a result. Investigation 1 For investigation 1, the mass of the glider was measured and found to be .373kg with an uncertainty of ±0.0005kg. The glider was then sat on an air track attached to either end of the track with springs, each with a spring constant 1.1N/m. With the springs acting as restorative forces, the glider is continuously stretching one while compressing the other. Therefore, there is always a spring force pulling on the glider, as the spring stretches farther the force increases because this produces the simple harmonic motion. In the first investigation, the air was turned on, creating a surface with little friction, and the glider was steadied in a position where it would move very little to determine its equilibrium position; this [Show More]

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