The graph shows the variation of displacement of aparticle executing SHM with time. We infer fromthi

The graph shows the variation of displacement of a particle executing SHM with time. We infer from this graph that

In mechanics and physics, simple harmonic motion is a special type of periodic motion or oscillation motion where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement.
Mathematically, the restoring force F is given by

F = –kx
where F is the restoring elastic force exerted by the spring (in SI units: N), k is the spring constant (N·m−1), and x is the displacement from the equilibrium position (m).
Value of phase constant depends on displacement and velocity of particle at time t=0.
The knowledge of phase constant enables us to know how far the particle is from equilibrium at time t=0. For example,
If φ=0 then from equation 4
x=A cosωt
that is displacement of oscillating particleis maximum , equal to A at t=0 when the motion was started.
What is Simple Harmonic Motion?
Simple Harmonic Motion or SHM is defined as a motion in which the restoring force is directly proportional to the displacement of the body from its mean position. The direction of this restoring force is always towards the mean position. The acceleration of a particle executing simple harmonic motion is given by, a(t) = -ω2 x(t). Here, ω is the angular velocity of the particle.

Table of Contents
Difference Between Simple Harmonic, Periodic and Oscillation Motion
Types of Simple Harmonic Motion
General Terms
Differential Equation
Angular SHM
Quantitative Analysis
Necessary conditions
Energy in SHM
Geometrical Interpretations
Horizontal Phasor
Simple Harmonic, Periodic and Oscillation Motion
Simple harmonic motion can be described as an oscillatory motion in which the acceleration of the particle at any position is directly proportional to the displacement from the mean position. It is a special case of oscillatory motion.

All the Simple Harmonic Motions are oscillatory and also periodic but not all oscillatory motions are SHM. Oscillatory motion is also called the harmonic motion of all the oscillatory motions wherein the most important one is simple harmonic motion (SHM).
Difference between Periodic, Oscillation and Simple Harmonic Motion
Periodic Motion
A motion repeats itself after an equal interval of time. For example, uniform circular motion.
There is no equilibrium position.
There is no restoring force.
There is no stable equilibrium position.
Oscillation Motion
To and fro motion of a particle about a mean position is called an oscillatory motion in which a particle moves on either side of equilibrium (or) mean position is an oscillatory motion.
It is a kind of periodic motion bounded between two extreme points. For example, Oscillation of Simple Pendulum, Spring-Mass System.
The object will keep on moving between two extreme points about a fixed point is called mean position (or) equilibrium position along any path. (the path is not a constraint).
There will be a restoring force directed towards equilibrium position (or) mean position.
In an oscillatory motion, the net force on the particle is zero at the mean position.
The mean position is a stable equilibrium position.
Simple Harmonic Motion or SHM
It is a special case of oscillation along with straight line between the two extreme points (the path of SHM is a constraint)
Path of the object needs to be a straight line
There will be a restoring force directed towards equilibrium position (or) mean position
Mean position in Simple harmonic motion is a stable equilibrium.
Types of Simple Harmonic Motion
SHM or Simple Harmonic Motion can be classified into two types,

Linear SHM
Angular SHM
Simple Harmonic Motion Key Terms
Mean Position
Amplitude in SHM
Time Period and Frequency of SHM
Phase in SHM
Phase Difference
Simple Harmonic Motion Equation and its Solution
Angular Simple Harmonic Motion
Conditions for an Angular Oscillation to be Angular SHM
Quantitative Analysis of SHM
Equation of Position of a Particle as a Function of Time
Necessary conditions for Simple Harmonic Motion
Time Period of SHM
Velocity of particle executing Simple Harmonic Motion
Acceleration in SHM
Energy in Simple Harmonic Motion (SHM)
Kinetic Energy of a Particle in SHM
Potential Energy of SHM
Total Mechanical Energy of the Particle Executing SHM
Geometrical Interpretation of Simple Harmonic Motion
SHM as a Projection of Circular Motion
Problem-Solving Strategy in Horizontal Phasor
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