Simple Harmonic Motion (the Simple Pendulum)

Simple Harmonic Motion (The Simple Pendulum)

Posadas, Roi Fidelis E.

Bachelor of Science in Biology – Human Biology

De La Salle University-Dasmariñas

Dasmariñas, Cavite Philippines

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ABSTRACT

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In mechanics and physics, simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement. It can serve as a mathematical model of a variety of motions, such as the oscillation of a spring. In addition, other phenomena can be approximated by simple harmonic motion, including the motion of a simple pendulum as well as molecular vibration. In this experiment, simple harmonic motion was studied using a simple pendulum and experimental determination of the magnitude of acceleration due to gravity was created. A simple pendulum is a small body suspended by a cord of negligible mass. When it is placed from its equilibrium position and released, it will execute a periodic motion. Period is given by the formula T= 2π√L/g, where L is the length of the pendulum and g is the magnitude of acceleration due to gravity. The equation of a straight line in a (period)2 – length curve whose slope is 4 π2/g is T2 = 4 π2 (L/g). Angular frequency and linear frequency can be determined using w = √g/L and f = (1/2 π)g/L. Conclusions were made that in simple pendulum, the period T is independent of the mass of the pendulum provided it vibrates in a vacuum. Air resistance has more effect on a bob made of cotton than it does on a bob made of solid metal. Also, the period is independent of the amplitude if it is small say 10-degress or less. Another is, the period is directly proportional to the square root of its length. This means that with two pendulums, one 16cm long and the other is 64cm long, the period of the longer one will be twice that of the shorter one. Lastly, the period is inversely proportional to the square root of...