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University Physics III · Oscillations · 1.09

Driven oscillations and resonance

Transient plus steady state under sinusoidal driving, response at the drive frequency, an amplitude peak near ω₀ pulled below it by damping, a phase lag near zero well below ω₀, exactly π/2 at ω₀ whatever the damping, and approaching π well above, with peak height and width set by Q and the linear single-frequency assumption the response curve rests on.

Course-map guide · not a complete lesson or simulation

Scope & orientation

What this subsection covers

Transient plus steady state under sinusoidal driving, response at the drive frequency, an amplitude peak near ω₀ pulled below it by damping, a phase lag near zero well below ω₀, exactly π/2 at ω₀ whatever the damping, and approaching π well above, with peak height and width set by Q and the linear…

A strong response uses x, v, and a versus time on shared axes and states where the model stops being reliable.

Reasoning checklist

Evidence, assumptions and limits

01

Assumptions to state

State the system, observable, approximation, and conditions held fixed before using a model.

02

Evidence to collect

Over what mass and amplitude range does T = 2π√(m/k) predict a real spring oscillator's period, and what does the residual pattern reveal?

Read the complete note

Over what mass and amplitude range does T = 2π√(m/k) predict a real spring oscillator's period, and what does the residual pattern reveal? Useful evidence includes period data across masses and amplitudes, a linearized T²-versus-m fit, an intercept converted to the spring's effective mass and compared with the predicted one third of the spring's own mass, residuals, and a stated range of validity.

03

Limits to state

This GioPhysics course map is an adaptable learning sequence, not academic credit, accreditation, or a universal university syllabus.

Read the complete note

This GioPhysics course map is an adaptable learning sequence, not academic credit, accreditation, or a universal university syllabus. Third-semester content is the least standardised of the introductory sequence: departments place oscillations, waves, optics, and thermal physics differently, and the modern-physics units here are a bounded survey rather than a complete course in relativity, quantum mechanics, atomic, nuclear, or particle physics. Follow your institution's published scope, notation, laboratory programme, and assessment rules. A result should be checked against units, signs, limiting cases, and the conditions under which its model was derived.

Diagram & examples

Work the claim before choosing an equation

Interactive concept map

Follow the model from claim to evidence.

01 · Physical claimDriven oscillations and resonance

Transient plus steady state under sinusoidal driving, response at the drive frequency, an amplitude peak near ω₀ pulled below it by damping, a phase lag near zero well below ω₀, exactly π/2 at ω₀ whatever the damping.

Read the complete note

Transient plus steady state under sinusoidal driving, response at the drive frequency, an amplitude peak near ω₀ pulled below it by damping, a phase lag near zero well below ω₀, exactly π/2 at ω₀ whatever the damping, and approaching π well above, with peak height and width set by Q and the linear single-frequency assumption the response curve rests on.

02 · RepresentationThe subsection's claim

Model, evidence, and boundary

03 · TestPrediction before measurement

What is the strongest test of a claim about Driven oscillations and resonance?

04 · Evidence & boundaryDecide, then qualify

Over what mass and amplitude range does T = 2π√(m/k) predict a real spring oscillator's period, and what does the residual pattern reveal?

Read the complete note

Over what mass and amplitude range does T = 2π√(m/k) predict a real spring oscillator's period, and what does the residual pattern reveal? Useful evidence includes period data across masses and amplitudes, a linearized T²-versus-m fit, an intercept converted to the spring's effective mass and compared with the predicted one third of the spring's own mass, residuals, and a stated range of validity.

Interactive diagram for Driven oscillations and resonance: follow the physical claim through its representation, proposed test, evidence, and model boundary.

modelModel, evidence, and boundary turns the stated idea into a representation that can make a prediction.

Example questions

Try the reasoning before revealing the structure.

Diagram check

What is the strongest test of a claim about Driven oscillations and resonance?

Quick check

Test the reasoning, not recall

What is the strongest test of a claim about Driven oscillations and resonance?

Choose an answer to test the model.