# Simple Pendulum Essay

2338 WordsMar 17, 201210 Pages
LAB REPORT Factors affecting Time period on a Simple Pendulum Introduction: Background: 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. Simple harmonic motion is typified by the motion of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's Law, or illustrated by the repeated movement of a simple pendulum. The motion is sinusoidal in time and demonstrates a single resonant frequency. This effect was first noticed by Galileo in 1581. He watched the lamps in Pisa’s cathedral swinging backwards and forwards. The time for each swing stayed almost the same even as the swinging died down. Galileo realized that this regular pattern could be used for time keeping. Therefore when an object oscillates with constant time period even if the amplitude varies, we say it is moving with simple harmonic motion (SHM). Hypothesis: In any system where there is a restoring force (Hooke’s law: F = -kx) or a restoring torque that tends to move the system back towards an equilibrium position, the system will tend to oscillate. When the restoring force or torque is proportional to the displacement from equilibrium, given by: x = x max cos(ωt) where ω is the angular frequency. The angular frequency is related to the frequency, f, and the period, T, by the equation: ω = 2πf = 2π / T Two examples of systems experiencing simple harmonic motion are a mass on a spring, where the spring provides the restoring force that is proportional to the displacement, and a pendulum, where the restoring torque