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# Difference Between Simple Pendulum and Compound Pendulum

Simple Pendulum vs Compound Pendulum

Pendulums are a type of objects which displays periodic oscillatory motions. The simple pendulum is the basic form of the pendulum, which we are more familiar with, whereas the compound pendulum is an extended form of the simple pendulum. Both of these devices are very important in the understanding of fields such as classical mechanics, waves and vibrations and other related fields in physics. In this article, we are going to discuss what simple pendulum and compound pendulum are, their operation, the mathematical formulae that describe the motion of simple pendulum and compound pendulum, the applications of these two, the similarities between simple pendulum and compound pendulum, and finally the difference between simple pendulum and compound pendulum.

Simple Pendulum

The simple pendulum consists of a pivot, a string and a mass. For ease of calculations, the string is assumed to be non-elastic and have zero mass, and the air viscosity on the mass is negligible. The string is pivoted, and the mass is hung by the string so that it can oscillate freely. The only forces that act on the mass are the gravitational force and the tension of the string. The motion of a simple pendulum for very small angles is said to be in the form of simple harmonic oscillations. The simple harmonic motion is defined as a motion taking the form of a = – (ω^2) x where “a” is the acceleration and “x” is the displacement from the equilibrium point. The term ω is a constant. A simple harmonic motion requires a restoring force. In this case, the restoring force is the conservative force field of gravitation. The total mechanical energy of the system is conserved. The period of oscillation is given by  where l is the length of the string and g is the gravitational acceleration. If viscosity or any other damping force is present, the system is identified as a damped oscillation.

Compound Pendulum

The compound pendulum, which is also known as the physical pendulum, is an extension of the simple pendulum. The physical pendulum is any rigid body that is pivoted so that it can oscillate freely. The compound pendulum has a point called the center of oscillation. This is placed at a distance L from the pivot where L is given by L = I/mR; here, m is the mass of the pendulum, I is the moment of inertia over the pivot, and R is the distance to the center of mass from the pivot. The period of oscillation for the physical pendulum is given by T = L is known as the length of gyration.

 What is the difference between Simple and Compound Pendulums? • The period and, therefore, the frequency of the simple pendulum depends only on the length of the string and the gravitational acceleration. The period and the frequency of the compound pendulum depend on the length of gyration, the moment of inertia, and the mass of the pendulum, as well as the gravitational acceleration. • The physical pendulum is the real life scenario of the simple pendulum.

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