Spring-Mass Energy Bar Chart
Animated spring-mass SHM with real-time KE/PE/Total energy bar chart. PE = ½kx², KE = ½mv². Optional damping shows energy loss.
ENERGY IN A SPRING-MASS SYSTEM
In an oscillating spring-mass system, energy constantly transforms between elastic potential energy () and kinetic energy (). When the spring is at maximum displacement (amplitude), all energy is . When it passes through the equilibrium position, all energy is . The total mechanical energy () remains constant in the absence of friction, following the Law of Conservation of Energy.
HOW TO USE THIS VISUALIZATION
1. **Stretch or Compress the Spring**: Drag the mass to set the initial amplitude. 2. **Run Simulation**: Observe the real-time energy bar chart showing the exchange between and . 3. **Vary the Spring Constant**: Notice how a stiffer spring () stores more energy for the same displacement. 4. **Add Damping**: Observe how thermal energy increases as mechanical energy is dissipated.
CORE FORMULAS
AP EXAM CONNECTION
Unit: Unit 7: Oscillations (Topic 7.1)
Learning Objective: 7.1.2
COMMON MISCONCEPTIONS
- Thinking potential energy is zero at maximum displacement.
- Believing kinetic energy is maximum when displacement is maximum.
- Assuming total energy changes during an ideal oscillation.
KEY TAKEAWAYS
- In simple harmonic motion, total energy is constant.
- Potential energy is maximum at the amplitude (displacement ).
- Kinetic energy is maximum at the equilibrium position.
- Stiffer springs store more elastic potential energy for a given displacement.
PRACTICE QUESTIONS
Q1 (QUANTITATIVE): A mass on a spring with N/m is stretched 0.2 m. What is its maximum kinetic energy?
Show Answer & Explanation
Answer: 2.0 J
Explanation: J.
