# Simple Harmonic Motion vs. Periodic Motion — What's the Difference?

By Tayyaba Rehman — Published on November 4, 2023

**Simple Harmonic Motion (SHM) is a specific type of Periodic Motion where force is proportional and opposite to displacement. Periodic Motion repeats itself at regular intervals, not always adhering to SHM's restoring force law.**

## Difference Between Simple Harmonic Motion and Periodic Motion

### Table of Contents

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## Key Differences

Simple Harmonic Motion (SHM) is characterized by motion that occurs when the restoring force and displacement are proportional and opposite. On the contrary, Periodic Motion involves motion that repeats at consistent intervals but doesn't mandate a specific relationship between force and displacement. SHM is, in essence, a subset of Periodic Motion, meaning all SHM is Periodic Motion, but not all Periodic Motion qualifies as SHM.

SHM is intrinsically tied to an equilibrium position, where the object in motion constantly oscillates back and forth around this point, and the force exerted on the object is proportional to its displacement from equilibrium. However, Periodic Motion, while also revolving around repetitive movement, doesn’t inherently imply a proportionality between restoring force and displacement. This distinction is crucial in physics when delineating between general repetitive motions and those specifically adhering to SHM principles.

Dissecting SHM further, it's governed by Hooke's Law, which states that the force F exerted by a spring is equal to the product of its spring constant k and the displacement x from its equilibrium position: F = -kx. Periodic Motion, however, is not restricted by such explicit mathematical relationships, allowing for a broader array of motion types (e.g., circular) under its umbrella. This broad vs. specific applicability characterizes the different analytical utilities of SHM and Periodic Motion.

A classic example of SHM is a mass-spring system, where an object attached to a spring experiences a restoring force propelling it towards equilibrium whenever displaced. Meanwhile, the rotation of the Earth constitutes Periodic Motion, as it repeats annually but isn't dictated by a restoring force directly proportional to displacement. The Earth's motion adheres to gravitational and celestial mechanics, diverging it from the nuanced mechanical principles dictating SHM.

Elucidating further, the unique attributes of SHM, like its sinusoidal position-time graph and symmetrical oscillations, are not ubiquitous in all Periodic Motion types. Some Periodic Motions may exhibit non-symmetrical, non-sinusoidal, or erratic oscillations while still repeating over time, proving the inclusive nature of Periodic Motion in encapsulating various movement forms, including but not confined to SHM.

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## Comparison Chart

### Nature of Force

Restoring force proportional to displacement

No obligation for proportional restoring force

### Example

Oscillation of a mass on a spring

Earth's rotation around the sun

### Position-Time Graph

Always sinusoidal

Can be non-sinusoidal

### Mathematical Equation

F = -kx (Hooke’s Law)

No universal equation

### Universality

A subset of Periodic Motion

Encompasses all repetitive motions including SHM

## Compare with Definitions

#### Simple Harmonic Motion

Simple Harmonic Motion is periodic motion centralized around an equilibrium.

The oscillation of a pendulum represents Simple Harmonic Motion.

#### Periodic Motion

Periodic Motion does not necessitate a proportional restoring force.

The periodic flashing of a lighthouse doesn’t follow a proportional restoring force.

#### Simple Harmonic Motion

Simple Harmonic Motion exhibits sinusoidal position-time graphs.

A mass-spring system in Simple Harmonic Motion displays a sine wave when graphed.

#### Periodic Motion

Periodic Motion manifests through cycles, oscillations, or rotations.

A swinging pendulum completes cycles, demonstrating Periodic Motion.

#### Simple Harmonic Motion

Simple Harmonic Motion follows Hooke's Law in mechanical contexts.

The extension of a spring demonstrates Simple Harmonic Motion as it adheres to Hooke’s Law.

#### Periodic Motion

Periodic Motion involves repetitive motion at regular intervals.

The orbit of a planet is an example of Periodic Motion.

#### Simple Harmonic Motion

Simple Harmonic Motion is characterized by a restoring force proportional to displacement.

In Simple Harmonic Motion, the further it is from equilibrium, the stronger the restoring force.

#### Periodic Motion

Periodic Motion can encompass various forms of movement, including rotations.

The spinning of a wheel exhibits Periodic Motion.

#### Simple Harmonic Motion

Simple Harmonic Motion involves symmetrical oscillations about an equilibrium point.

The equilibrium oscillations of a floating buoy showcase Simple Harmonic Motion.

#### Periodic Motion

Periodic Motion includes motions that repeat in space and time.

The regular pulsing of a star illustrates Periodic Motion.

## Common Curiosities

#### What defines Simple Harmonic Motion?

Motion with a restoring force directly proportional and opposite to displacement.

#### Is all Simple Harmonic Motion also Periodic Motion?

Yes, all SHM is a form of Periodic Motion.

#### How is Periodic Motion characterized?

By any motion that repeats itself at regular time intervals.

#### Does all Periodic Motion adhere to Hooke’s Law?

No, only SHM, a subset of Periodic Motion, adheres to Hooke’s Law.

#### Can Simple Harmonic Motion include rotational movements?

SHM typically involves linear oscillations, not rotations.

#### How does a position-time graph of Simple Harmonic Motion look?

It is sinusoidal, showcasing symmetric oscillations.

#### How does the restoring force in Simple Harmonic Motion behave?

It’s always proportional and opposite to displacement.

#### Can you provide an example of Periodic Motion that isn’t SHM?

The Earth’s orbit around the Sun is Periodic but not SHM.

#### Can Periodic Motion exhibit non-sinusoidal patterns?

Yes, Periodic Motion can display various waveform patterns.

#### Why is equilibrium significant in discussing Simple Harmonic Motion?

Because SHM oscillates symmetrically about an equilibrium point.

#### What dictates the repetitiveness of Periodic Motion?

Periodic Motion repeats due to consistent mechanical or dynamic conditions.

#### Can Periodic Motion be seen in celestial mechanics?

Yes, such as the consistent orbit of planets.

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Written by

Tayyaba RehmanTayyaba Rehman is a distinguished writer, currently serving as a primary contributor to askdifference.com. As a researcher in semantics and etymology, Tayyaba's passion for the complexity of languages and their distinctions has found a perfect home on the platform. Tayyaba delves into the intricacies of language, distinguishing between commonly confused words and phrases, thereby providing clarity for readers worldwide.