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Physics

Hooke's Law

The restoring force exerted by an ideal linear spring.

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Source & review

Difficulty

Beginner

Read time

5 min

Prerequisites

Forces, displacement, and sign conventions

Review statusNeeds review

Source

OpenStax, University Physics Volume 1, §15.1: Simple Harmonic Motion

Reference for the linear restoring-force relation. Explanation and worked example written for FormuLab.

Definition
Understanding the core concept

Stretching or compressing a linear spring produces a force opposing that deformation. The minus sign records this restoring direction: a positive extension produces a negative spring-force component. A larger stiffness means more force for the same deformation. A real spring may stop following this relation outside its linear range.

Variables & Units
Understanding each component
SymbolMeaningUnits
Signed spring-force component on the object
Spring stiffness (spring constant)
Signed deformation from the relaxed spring length
Real-World Applications
Where this formula is used in practice

Spring loading

Estimate the force at a specified elastic deformation.

Force gauges

Relate a calibrated spring's extension to force magnitude.

Vibration models

Write the spring-force term in a mass-spring model.

Worked Example
Step-by-step calculation with real numbers

Problem

An ideal spring has stiffness 250.0 N/m and is stretched 4.00 cm in the positive x-direction from its relaxed length. Find the spring-force component on the attached object.

Given

Solution

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Final Answer

FormuLab is a study reference. Verify formulas, units, assumptions, and course-specific conventions before relying on them.

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