University Physics III · Oscillations · 1.02
The SHM equation of motion and its general solution
Turning m d²x/dt² = −kx into d²x/dt² = −ω²x, verifying x = A cos(ωt + φ) by substitution, fixing A and φ from initial position and velocity, eliminating time to reach v = ±ω√(A² − x²), and noting that superposing solutions works only while the equation stays linear.
Course-map guide · not a complete lesson or simulationScope & orientation
What this subsection covers
Turning m d²x/dt² = −kx into d²x/dt² = −ω²x, verifying x = A cos(ωt + φ) by substitution, fixing A and φ from initial position and velocity, eliminating time to reach v = ±ω√(A² − x²), and noting that superposing solutions works only while the equation stays linear.A strong response uses energy-versus-displacement parabolas and states where the model stops being reliable.
Reasoning checklist
Evidence, assumptions and limits
Assumptions to state
State the system, observable, approximation, and conditions held fixed before using a model.
Evidence to collect
How do the damping constant and the drive frequency reshape steady-state amplitude, phase lag, and the time the transient takes to die away?
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How do the damping constant and the drive frequency reshape steady-state amplitude, phase lag, and the time the transient takes to die away? Useful evidence includes numerically integrated trajectories, an amplitude-versus-frequency sweep at several damping values, a phase-versus-frequency sweep tested against the π/2 crossing at ω₀, fitted peak positions and widths, and comparison with the linear-response prediction.
Limits to state
This GioPhysics course map is an adaptable learning sequence, not academic credit, accreditation, or a universal university syllabus.
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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.
Model, evidence, and boundary
When should a model used for The SHM equation of motion and its general solution be revised?
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.
When should a model used for The SHM equation of motion and its general solution be revised?
Quick check
Test the reasoning, not recall
When should a model used for The SHM equation of motion and its general solution be revised?
Choose an answer to test the model.