---
title: "Displacement from Equilibrium — AP Physics 1 Definition"
description: "Displacement from equilibrium is an object's distance and direction from where net force is zero; in SHM the restoring force is proportional to it (ma = -kΔx)."
canonical: "https://fiveable.me/ap-physics-1-revised/key-terms/displacement-from-equilibrium"
type: "key-term"
subject: "AP Physics 1"
unit: "Unit 7"
---

# Displacement from Equilibrium — AP Physics 1 Definition

## Definition

Displacement from equilibrium (Δx) is the distance and direction of an object's position measured from its equilibrium position, the spot where net force is zero. Simple harmonic motion happens when the restoring force is proportional to this displacement and points back toward equilibrium (ma_x = -kΔx).

## What It Is

Displacement from equilibrium is exactly what it sounds like. You find the [equilibrium position](/ap-physics-1-revised/key-terms/equilibrium-position "fv-autolink"), the location where the net force on the object is zero, and you measure how far (and in which [direction](/ap-physics-1-revised/unit-1/4-reference-frames-and-relative-motion/study-guide/iTcYEEULwbQlf2nW "fv-autolink")) the object currently sits from that spot. It's a vector, so a block stretched 5 cm right of equilibrium has a different displacement than one compressed 5 cm left, even though both are 5 cm away.

This quantity is the whole engine of [Unit 7](/ap-physics-1-revised/unit-7 "fv-autolink"). Per the CED, simple harmonic motion results when the magnitude of the restoring force is proportional to the displacement from equilibrium, captured in the derived equation ma_x = -kΔx. The negative sign is the restoring part. It tells you the force always points opposite the displacement, dragging the object back toward equilibrium. Pull the block right, the spring pulls left. Swing the pendulum left, gravity's component pushes right. That proportional, always-opposing relationship is the definition of SHM, and displacement from equilibrium is the variable everything else (force, acceleration, energy) gets written in terms of.

## Why It Matters

This term lives in [Topic 7.1](/ap-physics-1-revised/unit-7/1-defining-simple-harmonic-motion-shm/study-guide/GMUA9ME65plxVw8X "fv-autolink") (Defining Simple Harmonic Motion) and directly supports learning objective 7.1.A, which asks you to describe simple harmonic motion. You literally cannot state the SHM condition without it, because SHM is defined as [restoring force](/ap-physics-1-revised/key-terms/restoring-force "fv-autolink") proportional to displacement from equilibrium. It also explains why a pendulum only counts as SHM at small angular displacements; only then is the restoring force approximately proportional to displacement. Once you own this idea, you can read ma_x = -kΔx like a sentence instead of memorizing it, and you can predict where in the oscillation speed, acceleration, and force hit their max and min values.

## Connections

### Restoring force and Hooke's law (Units 2 and 7)

The spring force F = -kΔx you met with forces in [Unit 2](/ap-physics-1-revised/unit-2 "fv-autolink") becomes the restoring force in Unit 7. Same equation, new job. Displacement from equilibrium is the Δx in both, so doubling the displacement doubles the restoring force, which is the proportionality test for SHM.

### Energy in oscillating systems (Units 3 and 7)

Spring potential energy depends on the square of the displacement from equilibrium. So at maximum displacement the energy is all potential and the object is momentarily at rest, while at zero displacement the energy is all kinetic and [speed](/ap-physics-1-revised/key-terms/speed "fv-autolink") is at its maximum. Displacement from equilibrium is the dial that trades potential energy for kinetic energy.

### [Resonance (Unit 7)](/ap-physics-1-revised/key-terms/resonance)

[Resonance](/ap-physics-1-revised/key-terms/resonance "fv-autolink") is what happens when you drive an oscillator at its natural frequency and the displacement from equilibrium grows larger and larger with each push. You can't talk about a growing amplitude without first defining displacement from equilibrium as the thing that's growing.

## On the AP Exam

Multiple-choice questions love proportionality stems built on this term. A classic asks what happens to the restoring force if the displacement from equilibrium doubles (it doubles, because F is proportional to Δx), and that exact logic gets recycled for both mass-spring systems and small-angle pendulums. Another favorite asks which quantity is at maximum magnitude when displacement is zero (speed and kinetic energy, since force and acceleration are zero there). On the free-response side, the 2018 short-answer question about a block on a spring oscillating about the equilibrium position is the template. You need to identify where equilibrium is, describe force and acceleration as functions of displacement, and justify your reasoning with ma_x = -kΔx. The verbal skill being tested is connecting position in the cycle to the size and direction of the restoring force.

## displacement from equilibrium vs Amplitude

Displacement from equilibrium changes constantly during the motion. It can be anything from zero up to a maximum, and it has a direction. Amplitude is just the maximum magnitude of that displacement, a single fixed number for a given oscillation. So when a question says 'displacement from equilibrium is zero,' the object is passing through equilibrium at top speed. When it says 'displacement equals the amplitude,' the object is at a turning point, momentarily at rest with maximum restoring force. Mixing these up flips your answer about where speed and force peak.

## Key Takeaways

- Displacement from equilibrium is the distance and direction of an object's position relative to its equilibrium position, the point where the net force is zero.
- Simple harmonic motion is defined by the restoring force being proportional to displacement from equilibrium, written as ma_x = -kΔx.
- If displacement from equilibrium doubles, the restoring force doubles, for both mass-spring systems and small-angle pendulums.
- When displacement from equilibrium is zero, the restoring force and acceleration are zero but speed and kinetic energy are at their maximum.
- At maximum displacement (the amplitude), the object is momentarily at rest while restoring force and acceleration are at their largest.
- A pendulum only behaves as SHM at small angular displacements, because only then is the restoring force approximately proportional to displacement.

## FAQs

### What is displacement from equilibrium in AP Physics 1?

It's the distance and direction of an object's position measured from its equilibrium position, where net force is zero. In simple harmonic motion, the restoring force is proportional to this displacement and points back toward equilibrium (ma_x = -kΔx).

### Is the restoring force biggest when displacement from equilibrium is zero?

No, it's the opposite. At zero displacement the restoring force and acceleration are zero, while speed and kinetic energy are at their maximum. The restoring force is largest at maximum displacement, the turning points of the motion.

### How is displacement from equilibrium different from amplitude?

Displacement changes throughout the oscillation and has a direction, while amplitude is the fixed maximum magnitude of that displacement. An object's displacement can be anywhere from zero to the amplitude at any instant.

### What happens to the restoring force if displacement from equilibrium doubles?

The restoring force doubles too, because SHM requires the force to be directly proportional to displacement. This proportionality question shows up constantly in multiple choice for both springs and small-angle pendulums.

### Does a bigger displacement from equilibrium change the period of SHM?

No. For an ideal mass-spring system or small-angle pendulum, the period depends on the system's properties (like m and k, or pendulum length), not on how far you displace it. A bigger starting displacement means a bigger amplitude, not a longer period.

## Related Study Guides

- [7.1 Defining Simple Harmonic Motion (SHM)](/ap-physics-1-revised/unit-7/1-defining-simple-harmonic-motion-shm/study-guide/GMUA9ME65plxVw8X)

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