Simple Harmonic Motion (SHM): Definition, Equation, Types, Important Concepts and More


Simple Harmonic Motion (SHM) is a motion in which the restoring force is inversely correlated with the body's deviation from its mean position. This restorative power is always directed toward the mean position. A particle's acceleration in Simple Harmonic Motion is given by a(t) = -ω2 x(t). Here, ω is the particle's angular velocity.


On that note, let’s learn all important concepts related to Simple Harmonic Motion from the definition, equation, and types to differences with other oscillatory motions with examples in detail.

Simple Harmonic, Periodic and Oscillation Motion

Simple Harmonic Motion is an oscillatory motion in which the particle's acceleration at each position is directly proportional to its displacement from the mean position. It's a type of oscillation or oscillatory motion.


Simple Harmonic Motions (SHM) are all oscillatory and periodic, however not all oscillatory motions are SHM. Oscillatory motion is frequently referred to as the harmonic motion of all oscillatory motions, the most important of which is simple harmonic motion (SHM).


Simple Harmonic Motion is a very useful tool for understanding the characteristics of sound waves, light waves, and alternating currents. Any non-simple harmonic oscillatory motion can be expressed as a superposition of several harmonic motions of different frequencies.

Difference between Periodic, Oscillation and Simple Harmonic Motion

Periodic Motion

      A motion repeats itself after an equal time interval. Consider uniform circular motion.

      There is no place of equilibrium.

      No restorative force exists.

      There is no steady state of equilibrium.

Oscillation Motion

      A particle moving back and forth around a mean position is referred to as oscillatory motion when it moves on either side of the equilibrium or mean position.

      It is a particular type of periodic motion that is limited by two extremes. For instance, the Spring-Mass System or the Oscillation of a Simple Pendulum.

      The mean position (or equilibrium position) along any path is where an object will continue to move while oscillating between two extreme positions about a fixed point. The path itself is not a restriction.

      The equilibrium position (or mean position) will be the target of a restoring force.

      The net force acting on the particle in an oscillatory motion is zero at the mean position.

      A stable equilibrium position is the mean position.

Simple Harmonic Motion or SHM

      Between the two extreme points, it is a specific example of oscillation along a straight line (the path of SHM is a constraint).

      The thing must go in a straight line.

      The equilibrium position (or mean position) will be the target of a restoring force.

      A stable equilibrium exists at the mean position in simple harmonic motion.

Types of Simple Harmonic Motion

Simple Harmonic Motion, or SHM, can be divided into two categories:


      Linear Simple Harmonic Motion

      Angular Simple Harmonic Motion

Linear Simple Harmonic Motion

Simple harmonic motion is referred to when a particle oscillates in a straight line and around a fixed point (known as the equilibrium position).


Consider a spring-mass system.

Angular Simple Harmonic Motion

When a system oscillates angularly far from a fixed axis, an angular simple harmonic motion happens.

Terminology in Simple Harmonic Motion

Mean position

The mean position is typically defined as the position where the net or total force on the particle in SHM is zero.

Extreme Position

An extreme position is one that is situated at a distance equal to the amplitude of the Simple Harmonic Motion (SHM). At an extreme position, the velocity is typically zero and the acceleration is highest.


The greatest deviation from the mean position is referred to as the amplitude.


For a simple harmonic motion, phase is described as a quantity that falls inside the trigonometric function for a particle's position. Phase identifies the state of simple harmonic motion, which is its position and direction of motion.

Time Period

The time interval after which the particle returns to its initial phase is how the time period is defined or expressed.

Linear Frequency

Frequency is the Inverse of the time period.

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