Hooke’s Law Spring Oscillation Simulation with Damping and Energy
This interactive 3D physics simulation demonstrates
Hooke’s Law, simple harmonic motion,
air resistance, and energy transformation
in a vertical spring-mass system.
Hooke’s Law and Spring Motion
Hooke’s Law states that the restoring force of a spring is proportional to
the displacement from equilibrium:
F = -kx
The mass oscillates around its equilibrium position. Students can adjust
amplitude, spring constant, mass, and friction to observe how each parameter
affects the motion.
Damping and Air Resistance
The friction slider represents air resistance. When friction is increased,
the oscillation amplitude gradually decreases because mechanical energy is
converted into thermal energy.
F_d = -bv
A larger damping coefficient causes the motion to die out faster. With little
or no friction, the spring-mass system behaves more like ideal simple harmonic
motion.
Energy Transformation
The simulation includes colorful vertical energy bars showing kinetic energy,
spring potential energy, total mechanical energy, and thermal heat energy.
- Kinetic Energy: greatest near the equilibrium position.
- Spring Potential Energy: greatest near the turning points.
- Mechanical Energy: decreases when damping is present.
- Thermal Heat Energy: increases as friction removes mechanical energy.
E_total = KE + PE + E_thermal
Real-Time Graphs
A graph panel displays energy versus time and a phase-space graph of
displacement versus velocity. These graphs help students connect the visible
spring motion with mathematical models of oscillation and damping.
What Students Learn
- How spring constant affects oscillation frequency and period.
- How mass affects the speed of oscillation.
- How amplitude changes the size of the motion.
- How air resistance damps the motion over time.
- How mechanical energy transforms into thermal energy.
- How energy graphs and phase-space graphs describe oscillatory motion.
How to Use This Physics Simulation
- Use the amplitude slider to change the starting displacement.
- Increase the spring constant to make the oscillation faster.
- Increase the mass to make the oscillation slower.
- Use the friction slider to add air resistance and damping.
- Observe the energy bars and graphs as energy changes during the motion.
- Compare the ideal and realistic models.
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