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University Physics I · Oscillations · 14.05

Mass–spring systems

Horizontal and vertical springs, equilibrium shifts, effective stiffness, and combinations.

Course-map guide · not a complete lesson or simulation

Scope & orientation

What this subsection covers

Horizontal and vertical springs, equilibrium shifts, effective stiffness, and combinations.

A strong response uses energy-position graphs 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

How does period depend on oscillating mass, and where does the ideal model fail?

Read the complete note

How does period depend on oscillating mass, and where does the ideal model fail? Useful evidence includes period data across masses, a linearized model, effective-mass discussion, residuals, and uncertainty.

03

Limits to state

This GioPhysics course map is an adaptable teaching sequence, not a claim of accreditation or a universal university syllabus.

Read the complete note

This GioPhysics course map is an adaptable teaching sequence, not a claim of accreditation or a universal university syllabus. Departments can adjust the order, mathematical depth, laboratory hours, and optional fluids endpoint to match local requirements. 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 claimMass–spring systems

Horizontal and vertical springs, equilibrium shifts, effective stiffness, and combinations.

02 · RepresentationThe subsection's claim

Model, evidence, and boundary

03 · TestPrediction before measurement

Which response about Mass–spring systems is most defensible?

04 · Evidence & boundaryDecide, then qualify

How does period depend on oscillating mass, and where does the ideal model fail? Useful evidence includes period data across masses, a linearized model, effective-mass discussion, residuals, and uncertainty.

Interactive diagram for Mass–spring systems: 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

Which response about Mass–spring systems is most defensible?

Quick check

Test the reasoning, not recall

Which response about Mass–spring systems is most defensible?

Choose an answer to test the model.