Damped Harmonic Oscillation

Q: Why does a real pendulum eventually stop swinging?

Energy is dissipated due to damping forces. Air resistance and friction at the pivot do negative work on the system, converting mechanical energy into thermal energy.

Interactive 3D damped spring-mass simulator. Explore underdamped, critically damped, and overdamped regimes with live analytical charting and decay envelopes.

WHAT IS DAMPED OSCILLATION?

In the real world, mechanical systems eventually stop oscillating due to energy loss from friction, air resistance, or internal heating. This is known as damping. While ideal Simple Harmonic Motion (SHM) has a constant amplitude, a damped oscillator shows an amplitude that decreases over time.

TYPES OF DAMPING

1. **Underdamped**: The system oscillates with a decaying amplitude. 2. **Critically Damped**: The system returns to equilibrium as quickly as possible without oscillating. 3. **Overdamped**: The system returns to equilibrium slowly without any oscillation.

HOW TO USE THIS VISUALIZATION

1. **Set Damping Constant**: Adjust the friction level ().\n2. **Vary Mass/Spring**: Change the system parameters to see how inertia affects damping time.\n3. **View Graphs**: Observe the envelope curve that fits the decaying peaks of the displacement-time graph.\n4. **Toggle Energy**: Watch the total energy decrease as it is converted into heat.

CORE FORMULAS

Energy decay in a damped system

Linear damping force

AP EXAM CONNECTION

Unit: Unit 7: Oscillations (Topic 7.1)
Learning Objective: 7.1.2

COMMON MISCONCEPTIONS

Thinking damping changes the frequency significantly (it does for high damping, but not much for light damping).
Believing energy is destroyed (it is conserved, just converted to non-mechanical forms).
Confusing critical damping with zero damping.