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A simple pendulum executes a simple harmonic motion (SHM), that is, its periodic movement is defined by an acceleration which is proportional to its displacement and directed toward the centre of the movement.
Simple Pendulum
Simple Pendulum Definition
Simple pendulum is a mechanical system of mass which is connected to a long massless inextensible string which executes oscillatory motion. In ancient days, a pendulum was used to track the time. Pendulum is also used to identify the beats.
The time period of the pendulum is constant even when the amplitude is changed but when the gravitational acceleration changes then the time period of the simple pendulum also changes. This property is used to determine the acceleration due to gravity. The time period depends on the length of string to which the Bob of the simple pendulum is connected.
Simple Harmonic Motion (SHM)
The motion of an object moving back and forth along a straight line about an intermediate (mean) position is called simple harmonic motion. A pendulum experiences a simple harmonic motion. It oscillates back and forth about its centre position where the string and bob move. These motions of the pendulum are called oscillations, that represent simple harmonic motion.
A simple harmonic motion can be defined as an oscillatory motion where the acceleration of the particle at any position is proportional to the displacement from the mean position. It is a special case of oscillating motion.
Types of Simple Harmonic Motion
There are two types of Simple Harmonic Motion (SHM) which are given below.
- Linear Simple Harmonic Motion
- Angular Simple Harmonic Motion
Total Energy is Simple Pendulum
Mechanical energy is conserved in a simple pendulum. The total mechanical energy is a sum of kinetic energy and potential energy. When the pendulum moves back and forth, then there is a fixed exchange between kinetic energy and potential energy.
Kinetic Energy
The energy that an object possesses due to its motion is called the kinetic energy of that object. It depends on both mass as well as speed. For a simple pendulum, the kinetic energy increases as the pendulum reaches the equilibrium position, while on the other hand, as the bob of the pendulum moves farther from the equilibrium position, the kinetic energy decreases.
Kinetic energy of a simple pendulum is given as
Here,
v = velocity
m = mass
Potential Energy
The potential energy of a simple pendulum is given as
P.E.=mgh
Here,
g = gravitational acceleration
h = height
Mechanical Energy
Mechanical energy is the combination of kinetic and potential energy.
Therefore,
Oscillatory Motion
When an object repeatedly moves across a point, then the object movement is an oscillating movement. In a complete vacuum, the ideal state can be achieved because there is no air to stop the object in the friction of the oscillating motion.
Bob of a Simple Pendulum
A simple pendulum contains a small metallic ball or a piece of stone which is suspended on a rigid stand with the help of a thread called Bob of Pendulum.
Effect of Gravity on Simple Pendulum
We know, the time period is given as
Therefore, the time period of a simple pendulum is inversely proportional to the square root of gravitational acceleration.
Thus,
Hence, when the gravitational acceleration increases then the time period of simple pendulum decreases.
Time Period of Simple Pendulum
The time period of the pendulum does not depend on the size or mass of the pendulum, but on the length of the pendulum and the earth’s gravitational factor.
Calculation of gravitational acceleration of Simple Pendulum
Gravitational acceleration is determined experimentally by using a simple pendulum.
Time period (T) for a simple pendulum is not depend on mass or the elementary angular displacement, but only depends on the length (L) of string and the value of Gravitational acceleration.
Applications of Simple Pendulum
There are many applications of simple pendulums, some of which are given here.
- Simple pendulum is used in clocks because the time period of the pendulum is fixed, thus it is used to track the time.
- Pendulums are used to determine the gravitational acceleration.
Conclusion
Simple pendulum is a mechanical system of mass which is connected to a long massless inextensible string which executes oscillatory motion.
The motion of an object moving back and forth along a straight line about an intermediate (mean) position is called simple harmonic motion.
There are two types of Simple Harmonic Motion (SHM) which are given below.
- Linear Simple Harmonic Motion
- Angular Simple Harmonic Motion
Kinetic energy of a simple pendulum is given as
