The Formula For SHM

Simple Harmonic Motion is a fundamental idea in high school physics since it covers a wide range of issues that were formerly considered ground-breaking discoveries in the field. The pendulum is the most frequent example of simple harmonic motion. The restoring force is the most often associated phrase with simple harmonic motion. The SHM is another abbreviation for the SHM. 

Harmonic motion is defined as a function of a single sine, or cosine function is known as harmonic function. This comprehensive guide on SHM will explain simple harmonic motion formula, shm equation, etc.

What Is Simple Harmonic Motion?

When an object or particle is under a to and fro motion due to a restoring force that is dependent on the displacement from the mean position and the force is directed towards the mean position. This motion is nothing but Simple Harmonic Motion.

Some day to day examples of SHM are as follows-: 

• The vibration of the tuning fork 
• Oscillations from a freely suspended magnet. 
• The vibration of balance wheel of the watch 
• Oscillation of a loaded spring having stress energy. 

Hooke’s Law

One of the essential laws in the notions of friction and elasticity is Hooke’s Law. It

is one of the physic’s most fundamental and straightforward rules. In fact, this rule is a

perfect match for the equation of simple harmonic motion that we examined

previously. The only difference between the equation and the law is the expression of the law.

According to this rule, the force necessary to return an item to its origin, or the restoring force, acting here is dependent on the displacement taken off the string. As a result, the spring constant was born, and it’s worth repeating that the sign is determined by the direction in which the spring is traveling. If it’s traveling ahead, we put a positive sign on it, and if it’s heading backward, we put a negative sign on it.

Characteristics of Simple Harmonic motion

• The motion of the particle is periodic
• It is the most basic type of oscillatory motion.
• The particle oscillates about the mean position with fixed amplitude and fixed frequency.
• The simple harmonic motion is defined by the single function of sine or cosine.

Terminologies Related To Simple Harmonic motion

• Displacement – It is defined as the distance covered by the oscillating particle from the mean position at any instant t. It is represented by x.

• Amplitude – It is defined as the maximum displacement of the oscillating particle from the mean; the position is denoted by A and x max = +/- A

• Time period- It is defined as the time taken to complete one oscillation.
• Frequency -It is defined as the number of oscillations completed per unit time. It is denoted by v( nu). Frequency is one upon divided by the time period.

• Angular Frequency- it is obtained by multiplying 2π with v . It is denoted by ( omega ) = 2π/T=2πv

• Phase – The phase of a particle is defined as the state of the particle with regard to the position and direction of motion at a particular instant. For example, in the equation

x= A cos ( ωt +Φ0 )

where Φ =( ωt + Φ0)

• Oscillation- It is defined as the one complete back and forth motion of a particle that starts and ends at the same point.

Simple Harmonic Motion (SHM) Formulas

Let us consider a body oscillating from the mean position. The displacement by the body

occurs and let us consider the displacement is small and hence we can say –

The force under action is directly proportional to the displacement.

Which further can be written as

Restoring force is directly proportional to Displacement

F∝ x. Or

F = -kx ————————————–(1)

Where F = Restoring force

x = Displacement

K=Spring factor and force constant it is positive constant. It is given by restoring force per

unit displacement with SI unit is Nm-1.

Equation (1) defines Simple Harmonic Motion. The negative sign in this equation represents

the fact that the force F acts in the direction opposite to the direction of displacement x.

Based on the Second law of motion

F= ma—————————————–(2)

F= Force , m = mass of the object , a= Acceleration.

From (1) and (2) we can say

ma = -kx

a = -K/m * x

a ∝ x

Hence in simple harmonic motion, acceleration is directly proportional to its displacement

and the acceleration is directed to the mean position.

F= – kx

Where F = restoring force, K = spring factor , x = displacement

Conclusion

When we speak about the area of physics, one of the most significant notions is simple harmonic motion. It is the foundation of many other branches of physics, including differential mechanics, elasticity, and waves. Simple harmonic motion is a harmonic motion which means it can be represented in terms of single sine or cosine function further the simple harmonic motion is a periodic function wherein the displacement of the particle takes place to and fro about the mean position with the displacement of the body directly proportional to the restoring force. The particle oscillates with the fixed frequency and amplitude.