Energy in SHM –Kinetic and Potential Energies

Introduction

The ability to do work is called energy. Energy is required for every object to perform the job, and even when the object is at rest, it requires energy. Energy is such an important factor. The SI unit of energy is Joule. There are different forms of energy, such as kinetic energy and potential energy. In simple harmonic motion, an object possesses energy while traveling in the same path repeatedly. So, let us understand more about Simple harmonic motion, kinetic energy, potential energy, types of potential energy, the difference between kinetic and potential energy, and the examples of kinetic energy and potential energy.

Body

Energy in Simple Harmonic Motion

When the restoring force of a body is directly proportional to the displacement of the body from its mean position is known as Simple harmonic motion. For example, pendulum. When it is in motion, it moves toward the extreme position, and when it reaches the extreme position, it moves back towards the equilibrium point. There is always an exchange of kinetic energy and potential energy in simple harmonic motion. So, to calculate the energy in simple harmonic motion, we need first to calculate the kinetic energy and potential energy. Harmonic oscillator is the name of a system that performs simple harmonic motion.

Case 1. At the equilibrium point where the minimum displacement occurs, i.e., the kinetic energy is maximum, and potential energy is zero.

Case 2. At the maximum displacement point from the equilibrium point, i.e. the potential energy is maximum, and the kinetic energy is zero.  

The Kinetic energy in simple harmonic motion

When the object is in motion, the kinetic energy is possessed by the object.

v= ±ω √(a² – x²)

∴ v² = ω² ( a² – x²)

∴ Kinetic energy K.E. =  (½) mv² =  (½) m ω² ( a² – x²)

As, k/m = ω²

∴ k = m ω²

Kinetic energy=( ½) k ( a² – x²) 

The Potential energy in simple harmonic motion

When the object is at rest, the potential energy is possessed by the object. Consider the particle is performing the simple harmonic motion at a distance x from its mean position 0

W = – fdx = – (- kx)dx = kxdx

Total work done to displace the particle from 0 to x is 

∫dw= ∫kxdx = k ∫x dx

Total work done W = ( ½) k x² 

The total potential energy U = (½) kx² = (½) m ω²x²

Kinetic energy

When we apply any force on an object to work, the energy transferred to the object is known as kinetic energy when the work is done. Kinetic energy depends on mass and speed. The JouleJoule is the SI unit of kinetic energy. The formula for kinetic energy is 

KE= 1/2mv²

Some examples of kinetic energy

1. The kinetic energy is tremendous for an asteroid falling towards the earth.
2. The kinetic energy of a moving train is more due to its speedy velocity and large mass.
3. Flowing water has kinetic energy due to its mass and velocity. 

Types of kinetic energy

• Sound energy
• Thermal energy
• Radiant energy
• Electrical energy
• Mechanical energy

Potential energy

In the 19th century, Scottish engineer and physicist William Rankine introduced potential energy. There are different types of potential energy; each is related to a distinct force. The object needs energy for its resting position. Or the object stores some energy as a result of its position. For example, a bow and an arrow stores some energy when it is drawn, and when released, it is responsible for the gain of kinetic energy. The SI unit of all energies is the same. So, the SI unit of potential energy is also Joule.

The formula for potential energy is 

    W= mgh

Where m is the mass, g is acceleration, and h is the height.

Types of potential energy

There are two types of potential energy

1. Gravitational Potential energy
2. Elastic Potential energy

1. Gravitational Potential energy: When the object possesses the energy at a certain height against gravity is known as the gravitational potential energy. The formula to calculate Gravitational Potential energy is

W=mgh

2. Elastic Potential energy: When an object can store energy when stretched or compressed, the energy is known as elastic potential energy. For example, rubber, bungee cords, and trampoline. Some objects are designed to have more elastic potential energy. For example

• Coil spring of a wind-up clock.
• Twisted rubber band

The formula to calculate the elastic potential energy is 

     U= (½)kx²

Difference between Kinetic energy and potential energy

Kinetic energy

1. Kinetic energy is present in a particle when the particle is in motion.
2. We can easily transfer kinetic energy from one body to another.
3.  Velocity, speed, and mass are the determining factors of kinetic energy.
4. One of the examples of kinetic energy is flowing water.
5. Kinetic energy is relative to nature.

Potential energy

1. Potential energy is present in a particle when it is not in motion, i.e., in rest.
2. We can not transfer potential energy from one body to another.
3. Distance, height, and mass are the determining factor of potential energy.
4. One of the examples of potential energy is water present at the top of a hill.
5. Potential energy is non-relative concerning time.

Conclusion

We have studied Kinetic energy, potential energy, types of kinetic energy, types of potential energy, examples of kinetic energy and potential energy, the difference between kinetic energy and potential energy. So, it is clear that every object, body, or particle requires energy in the universe. Energy has different forms. Neither we can create energy, nor we can destroy. Some objects or bodies can store energy. The important forms of energy are kinetic energy and potential energy. These two energies are subdivided into different energies.