Simple harmonic motion

High School

Definition

A repetitive back-and-forth motion in which the restoring force is proportional to the displacement from the rest position and always directed toward it. A swinging pendulum and a mass on a spring are classic examples.

Worked examples

A mass on a spring: \(F = -kx\), where \(k\) is the spring constant and \(x\) is displacement from equilibrium.

The restoring force is proportional to displacement and points back toward the center — the signature of SHM.

A pendulum swinging with small angles: the restoring force from gravity is proportional to the angular displacement.

For small swings, the pendulum behaves as simple harmonic motion with a regular, repeating period.

Common mistakes

Any repeating motion is simple harmonic motion → Only motion where restoring force \(\propto\) displacement qualifies as SHM A car driving in circles repeats but has constant-magnitude centripetal force, not a restoring force proportional to displacement.
The restoring force pushes away from equilibrium → The restoring force always pulls toward the equilibrium position That's what makes the object oscillate back and forth through the center instead of flying off.
Amplitude affects the period of a mass-spring system → Period depends only on mass and spring constant, not amplitude In ideal SHM, larger swings take the same time as small ones — the motion is isochronous.

Where you'll use it next

Simple harmonic motion is foundational for studying waves, sound, AC circuits, and quantum mechanics. You'll apply it in advanced physics to analyze vibrations, resonance, and oscillatory systems in engineering and technology.

Found in 1 StudyPug lesson

Discover the Periodic Nature of SHM and Simple Pendulums

Physics 12

Dive into the world of periodic motion! Understand simple harmonic motion and simple pendulums through engaging visuals and real-world applications. Master these fundamental concepts in physics and mathematics.

12th Grade12th