Energy of Simple Pendulum

You may have seen pendulums in science classrooms. This motion is reminiscent of a simple demonstration of gravitational force – the more gravitational force, the longer the pendulum will swing back and forth. It’s probably worth thinking about what energy really means for a system like this. What does it mean to say that energy is conserved? What is the meaning of the change in energy? What is the energy formula? We will discuss all this in the article. The unknown constant in all the physics of a swinging pendulum is angular momentum, and the known one is the gravitational constant.

Simple Pendulum

A pendulum is a device with a bob or weight on the end of a rod which can be caused to rock back and forth, either by wind, the hand of an operator, or the force exerted by the earth. It will oscillate in one direction for some time, then in the other. 

A simple pendulum is a pendulum that has only two states of motion: from rest to top and from top to rest.

The features of a simple pendulum are as given below:

• Any oscillator with two degrees of freedom is called a simple pendulum.
• A point mass is attached to a rod, which is hinged on an axle or pivot at one end.
• The rod is of negligible mass.
• The string is of negligible mass and is held in place by some constraining mechanism at one end.

Energy

Energy is the property of objects which allows them to be changed or moved. It is required when a force acts upon an object to make it move, change its position, or change it in another way. 

There are several different types of energy. The word ‘energy’ can mean different things to different people (scientists and nonscientists), so this may not be surprising.

The Energy of Simple Pendulum

If a simple pendulum is hanging from a hinge, we can consider it at rest when the bob is vertically overhead and ask about its energy. If there is no force on the bob, it will swing back and forth forever with the same speed (and direction).

The energy of a simple Pendulum =mgh +  ½ mv2

The energy formula states that total energy equal to sum of  kinetic energy (½  mass times velocity squared) and potential energy ( weight multiplied by height and height equals diameter plus twice thickness).

The energy of the simple pendulum is in conserved form. We can’t make it do any work because its potential energy is determined by its height – we can shift it only with a small force, and the bob will not fall. We can increase the height, but it’s still impossible to do work. The important thing to note is that all the energy of a simple pendulum system is contained in either kinetic or potential energy.

In particular, the energy of the simple pendulum is fixed by Newton’s third law of motion, which implies that according to the conservation of energy, there is no exchange of any forms of energy between the pendulum (or other objects), and this is true for all systems that undergo simple harmonic oscillations.

Time Period Formula for Pendulum

The time period formula for a pendulum gives us a way to figure out a pendulum’s period if we know its length and weight.

The formula of time period: T = 2π√(L/g)

Where:

T is the time period that is twice the length of a full cycle. T is measured in seconds.

L is the length of string (from pivot to the point on the string directly under the bob).

g is the acceleration due to gravity, which is 9.81 m/s².

Moment of Inertia

Consider a simple pendulum with a mass of 10 grams hanging from its pivot point on a hinge. The pendulum’s angle from the bottom (that is, angular position) to its pivot point, with the hinge at rest, will be zero degrees. 

To find the moment of inertia (mass times length squared), we take the square root of (mass)2/l.

Conclusion

The energy of a simple pendulum is not constant, but it depends on the mass and length of the pendulum.

The energy formula of a simple pendulum is the total potential energy, kinetic energy, and mechanical energy.

About a simple pendulum, an important difference between mass and length of weight is that when you take up a pendulum from its resting position, you have to make it swing so that energy will be transformed into kinetic energy. The time period formula for the pendulum gives us an arithmetical definition of the period of the simple pendulum.