Nano PHYSICS . MECHANICS . WORK AND ENERGY . SPRING POTENTIAL ENERGY

Spring Potential Energy Function

From Hooke's law, the energy stored in an ideal spring is proportional to displacement squared relative to equilibrium.

Physics · Mechanics · Work and Energy · Spring Potential Energy · Spring Potential Energy Function
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Unsigned visitors can show & copy prompts for Steps 1-3. Signed-in free accounts can also Run with AI for Steps 1-2. Paid accounts unlock everything (Steps 1-6 + Help prompts + AI).
Steps 1-3 Free Steps 4-6 Paid
STEP 1
Orient: spring potential energy function
Free
Establish Hooke's-law and spring-energy ideas using equilibrium and displacement.
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Goal: define the ideal-spring model using equilibrium, displacement, force, stiffness, and energy.
STEP 2
Conceptual grounding: build the spring-energy model
Free
Build a workflow for spring force, stored energy, compression, extension, and release.
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Goal: distinguish restoring force from stored spring potential energy.
STEP 3
Real-world connection: interpret springs, launches, and storage
Free
Apply spring reasoning to ideal springs, energy storage, launches, multiple springs, and conservation.
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Goal: explain compression, extension, release, multiple springs, and conservation in physical contexts.
STEP 4
Check your understanding: diagnostic mini-quiz
Paid
Attempt each question before revealing the spring-energy reasoning.
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Goal: identify and correct equilibrium, sign, squared-displacement, and energy-bookkeeping errors before they become calculation errors.
STEP 5
Practice: solve increasingly rich spring-energy situations
Paid
Apply the model to situations that grow in complexity.
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Goal: write concise, physically justified spring-force and spring-energy explanations and solutions.
STEP 6
Summary & reflection + explorations
Paid
Consolidate the model and explore changing stiffness, displacement, systems, and conservation assumptions.
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🔒 ▶ Explore interactive simulation
Goal: carry the model forward into conservation of mechanical energy, oscillations, launches, and energy diagrams.