Analytical Analysis Of Simple Pendulum

Analytical analysis of simple harmonic motion using pendulum with varying conditions

Briz, Axel John, Salih, Nashreen Dale

Institute of Physical Sciences, College of Science, University of the Philippines Baguio

Abstract

This scientific investigation presents how simple harmonic motion happens in pendulum. Old pendulum clocks are basic example for pendulum that shows period and oscillation with respect to time. By using different masses, thread or string and protractors for angle calibration, this experiment was done. Twenty (20) back and forth movement was recorded with respect to the time it reached 20 periods. Each trial for 3 cases has resulted to relatively near oscillation per period. It was observed that whatever instances done, either play with the angles and masses for each trial, no abrupt or tremendous change was observed. Deviations for almost all cases were little to no value, nonetheless,

T = 2π√(L/g)), where T is the period of the pendulum, L is its length and g is the acceleration of gravity.[1]

Many things in nature wiggle in a periodic fashion through vibration. One such example is a simple pendulum. A simple pendulum may be described ideally as a point mass suspended by a massless string from some point about which it is allowed to swing back and forth in a place. When the mass is displaced a small angle from equilibrium and then released, the pendulum undergoes simple harmonic motion. Theoretically, the period of a pendulum is independent of its mass, and depends on length according to the power-law relationship

Tα√L

where T is the period of oscillation and L is the length. This result can be determined using a dimensional-analysis approach. The independence of mass is a result of the fact that all objects are accelerated towards the center of the earth with the same acceleration of