Unit 7 · Topic 06

Oscillations

Period, frequency, amplitude, and phase describe cycles without yet assuming simple harmonic motion.

Unit 7OscillationsOpen navigation

Concept 01

Maximum excursion

Essential The minimum you should retain

Amplitude A≥0 is the maximum of |x| from equilibrium.

UnderstandInterpret and connect

The sign belongs to x or phase, not to A.

DeepenFormulation and conditions

Extrema need not be symmetric if the model or equilibrium changes.

ExploreConnections for further study

Defining equilibrium first prevents measuring amplitude from the wrong origin.

Concept 02

Counting cycles

Essential The minimum you should retain

Period T is one-cycle time, and f=1/T measures cycles per second.

UnderstandInterpret and connect

Angular frequency is ω=2πf \omega=2\pi f =2π/T.

DeepenFormulation and conditions

Angular describes phase and does not require physical rotation.

ExploreConnections for further study

Changing time units changes the numerical representation, not the phenomenon.

Mathematical relation

Period and frequency

f=1T,ω=2πf=2πT f=1/T,\quad \omega=2\pi f=2\pi/T
Represents

Cycle and phase relations.

Physical interpretation

ω describes phase and does not require physical rotation.

DeepenVariables, conditions, and checks

Variables

f
frequency; usual unit: Hz
ω
angular frequency; usual unit: rad/s

Conditions of application

  • T>0.

Dimensional check

Hz and rad/s.

sinusoidal position model

Sinusoidal position with amplitude, period, and phase marked.phase φ+A−AT
  • x/A

A measures maximum displacement, T one cycle, and φ the initial phase.

Concept 03

Where the cycle is

Essential The minimum you should retain

Phase identifies the state within a cycle.

UnderstandInterpret and connect

Two oscillations may share A and T yet differ in phase.

DeepenFormulation and conditions

Initial phase encodes initial conditions together with amplitude.

ExploreConnections for further study

Synchronization and phase difference matter when comparing oscillators.

Concept 04

A broader category

Essential The minimum you should retain

Every ideal SHM is periodic, but not every periodic motion is SHM.

UnderstandInterpret and connect

SHM requires acceleration linear in and opposite to displacement.

DeepenFormulation and conditions

A repeating shape need not be sinusoidal.

ExploreConnections for further study

Damping or driving may change amplitude and phase over time.

Concept review

Common errors

Each warning includes a concrete way to review the reasoning, not only an incorrect-answer marker.

Equating every periodic motion with SHM.

SHM requires a∝−x.

Assuming oscillation frequency ω requires physical rotation.

ω describes phase rate.