Simple Pendulum 1 .pdf - QATAR UNIVERSITY Mathematics for...

QATAR UNIVERSITY
Mathematics for Engineering
Math 217-L51
Dr. Houssein Ayoub
Simple Pendulum
Alhanof AlNaemi
Fatima Alsulaiti

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Abstract
Simple pendulum or other types of pendulum have played a key role in many advancements in
the domain of physics, time measurement, climate and earthquake predictions and many other
applications.
One of the first clocks that could show time will relative accuracy were all dependent on a
pendulum continuous movement. The period of the oscillation was the main factor on which the
clock worked and it was adjusted in manner that a complete period was of 1sec.
The understanding of the motion of a simple pendulum is important as it gives insight to
understanding of objects motion under gravity, the inertial change in a body during its motion
and the effect of centripetal and external forces on the motion of a body. Thus, a complete
analysis of a simple pendulum motion gives a complete analysis of a simple harmonic motion
with forces in balance.

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Table of Contents
Abstract ............................................................................................................................................ 1
Table of Figures ............................................................................................................................... 2
Introduction ..................................................................................................................................... 3
Derivations and Results ................................................................................................................... 4
Conclusion ....................................................................................................................................... 9
Bibliography .................................................................................................................................... 9
Authors’ Contributions .................................................................................................................... 9
Table of Figures
Figure 1- Simple Pendulum (NAgle, 2012) ..................................................................................... 3

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Introduction
A simple pendulum is can be taken as a suspended mass attached to a spring or rod whose mass
can be neglected. The mass resonant at a fix frequency until the motion of the pendulum dies
down and it comes back to its original form. An illustration of a pendulum is shown below:
Figure 1- Simple Pendulum (NAgle, 2012)
The period of oscillation of the pendulum depends on the length of the string and the mass of
the suspended mass. The mass is resolved into its component and by using the newton’s second
law of torque equals to the rate of change of angular momentum a second order nonlinear
differential equation is derived. The nonlinear terms in the equation due to the component of
the mass along the direction of the motion. The main objective is to find an expression for the
time period of the pendulum using differential equations technique.