Simple Harmonic Motion

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Experiment 1: Simple Harmonic Motion Laboratory Report Ma. Zealina Salamat, Sittie Zuleiha Salik, Mary Grace Sumalinog, Paolo Gio Villar Department of Math and Physics College of Science, University of Santo Tomas España, Manila Philippines Abstract Introduction In addition to linear motion and rotational motion there is another kind of motion that is common in physics. This is the to and fro motion of oscillations or vibrations. When something oscillates, it moves back and forth with time. Simple harmonic motion can serve as a mathematical model of a variety of motions, such as the oscillation of a spring. Additionally, other phenomena can be approximated by simple harmonic motion, including the motion of a simple pendulum and molecular vibration. Simple harmonic motion provides the basis of the characterization of more complicated motions through the techniques of Fourier analysis. Simple Harmonic Motion arises when we consider the motion of a particle whose acceleration points towards a fixed point and is proportional to the distance of the particle from the fixed point. As the particle moves away from the fixed point it will slow down and eventually stop before returning to the fixed point. It will keep going and then again slow down before stopping. In this experiment, the force constant of the spring will be determined as well as the period of vibration of the spring executing simple harmonic motion. Also, the variations of kinetic energy as well as the potential energy versus time for the simple harmonic motion would be plotted and lastly, the conservation of energy for the simple harmonic motion would be verified. Theory An object moving along the x-axis is said to exhibit simple harmonic motion if its position as a function of time varies as x(t) = x0 + Acos(ωt + φ). The object oscillates about the equilibrium position x0.

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