An Idea On Simple Harmonic Motion

Simple harmonic motion is a concept in physics. The simple harmonic motion of an object is found by using a simple harmonic motion equation. Simple harmonic motion is a unique kind of periodic motion where the reestablishing force on the moving item is straightforwardly relative to the magnitude of the object’s displacement and acts towards the object’s equilibrium position. The simple harmonic motion contains three terms. Simple is a term used along with a word to convey that this is straightforward to understand. Harmonic in physics means a component frequency of a wave. A change in the position of an object is called motion.

The simple harmonic motion equation

Motion that repeats itself in equal intervals of time is called simple harmonic motion. The equation is a method for saying that one thing is equivalent to, or a similar worth as, another. A simple harmonic motion equation is the method for saying that motion that repeats itself in equal intervals of time is equivalent or similar. The acceleration is not constant in simple harmonic motion. So objects in simple harmonic motion do not obey the three equations of motion. The Simple harmonic motion equation of one-dimensional simple harmonic motion is given below.

Fnet = m (d2x /dt2) = -kx

Where, 

m = Inertial mass of the oscillating body.

x = Its displacement from the equilibrium position.

k = The spring constant for a mass on a spring.

This equation can also be written as follows.

(d2x / dt2) = -(k/m)x

Solving the above equation produces the following solution.

x(t) = c1 cos(wt) + c2 sin(wt)

From this simple harmonic motion equation, we can understand that in simple harmonic motion, the frequency and period are independent of the amplitude and the initial phase of the motion.

Simple harmonic motion formula

The formula is an exceptional condition that communicates a significant connection between factors communicating regularly utilized thoughts, similar to speed, temperature, and so forth. The various simple harmonic motion formulas are given below.

• General formula of SHM

Displacement x =A sin(ωt + Φ)

• Time Period (T)

T = 2π/ω

• Hooke’s law

Force (F) = -kx 

•  Acceleration (a)

a = -ω2x = -ω2 A sin(ωt + Φ)

• Angular Frequency (ω)

ω = 2π/T = 2πf

• Frequency (f)

f = 1/T = ω/2π

•  Kinetic Energy

K = ½ mω2(A2 – x2)

K = ½ k(A2 – x2)

• Springs in series

1/keq = 1/k1 + 1/k2

• Potential Energy

U = ½ kx2 (as a function of x)

• Simple Pendulum

T = 2π√l/g

• Springs in parallel

Keq = k1+k2

• Total Energy

E = U+K

E= ½ mω2

•  Physical Pendulum

T = 2π√I/mgl

• Torsional Pendulum

T = 2π√I/k

Frequency and wavelength of simple harmonic motion

Frequency and wavelength are conversely corresponding to one another. The wave with the greatest frequency has the most limited wavelength. Double the frequency implies one half of the wavelength. The frequency of simple harmonic motion is the number of times in which the wave occurs in one sec. The wavelength of the simple harmonic motion is the distance between two adjacent waves. 

The number of oscillations produced by the particle per unit is called the frequency of simple harmonic motion. In other words, the number of oscillations that a particle performs per unit of time is called the frequency of simple harmonic motion. The frequency of simple harmonic motion is calculated by dividing the number of times the event occurs by the length of time. The frequency of simple harmonic motion is denoted by hertz (in symbol Hz).

The wavelength of the simple harmonic motion is the distance from one peak to the next of a wave. wavelength is the distance a wave has travelled after one period or one complete cycle. Simple harmonic motion is periodic. So the wavelength of simple harmonic motion can be represented by a sine wave with constant amplitude and frequency. 

The wave of simple harmonic motion has the following form.

y=Acos((2π/λ)x−(2πt/T)+φ)

Where, 

A is the amplitude. 

λ is the wavelength.

T is the period. 

φ is the phase.

There are many real-life examples of simple harmonic motion. Some of the examples of simple harmonic motion are the following.

1. Swings in the park
2. Pendulum in the clock
3. Car Shock Absorber
4. Bungee Jumping
5. Hearing
6. The vibration of the string of a violin
7. Back and forth movement of the cradle
8. Atoms vibrating in molecules
9. Motion of spring
10. Oscillation of liquid in a U-tube

Conclusion

The Simple Harmonic Motion equation is the simplest equation in physics. The simple harmonic motion formula is significant because SHM is a specific sort of movement exceptionally normal in nature and emerges when the force on the swaying body is straightforwardly corresponding to the dislodging from its balance position and at any time of movement, this power is coordinated towards the balance position. In simple harmonic motion, force following up on the molecule is generally coordinated towards a decent point known as equilibrium position and the extent of power is straightforwardly relative to the relocation of the molecule from the equilibrium position.