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Driven Oscillator Interactive MicroSim

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About This MicroSim

This interactive simulation demonstrates the physics of driven (forced) oscillations. You can adjust the driving frequency, driving force amplitude, and damping to observe how the system responds, especially when near resonance.

Controls

Driving Frequency (ωd/ω₀)

  • Ratio of driving frequency to natural frequency
  • At ratio = 1.0, you're driving at resonance
  • Watch the amplitude grow dramatically at resonance!

Driving Force (F₀)

  • Amplitude of the periodic driving force
  • Larger force = larger steady-state amplitude

Damping (b)

  • Resistance that removes energy from the system
  • Higher damping = smaller resonance peak

What to Observe

At Resonance (ωd/ω₀ ≈ 1)

  • Amplitude builds up over time
  • Maximum energy transfer from driver to oscillator
  • Lower damping → higher amplitude

Below Resonance (ωd/ω₀ < 1)

  • Motion follows the driving force
  • Amplitude relatively small

Above Resonance (ωd/ω₀ > 1)

  • Motion opposes the driving force (180° phase shift)
  • Amplitude decreases as frequency increases

The Physics

The equation of motion for a driven damped oscillator:

m(d²x/dt²) + b(dx/dt) + kx = F₀cos(ωd·t)

Where: - m = mass - b = damping coefficient - k = spring constant - F₀ = driving force amplitude - ωd = driving angular frequency

Lesson Plan

Learning Objectives

By the end of this lesson, students will be able to:

  1. Explain the concept of resonance and identify when it occurs in a driven oscillator
  2. Predict how changes in driving frequency affect the amplitude of oscillation
  3. Analyze the role of damping in limiting resonance amplitude
  4. Apply the driven oscillator model to real-world examples (bridges, musical instruments, radio tuning)

Target Audience

  • High school physics students (grades 11-12)
  • Introductory college physics students
  • Prerequisites: Understanding of simple harmonic motion and damped oscillations

Activities

Activity 1: Discovering Resonance (10 minutes)

  1. Set damping to minimum (0.1 kg/s) and driving force to 10 N
  2. Slowly increase the frequency ratio from 0.5 to 1.5
  3. Record the maximum amplitude at each frequency
  4. Identify the frequency ratio that produces maximum amplitude

Activity 2: The Effect of Damping (10 minutes)

  1. Set frequency ratio to 1.0 (resonance)
  2. Run simulation with damping = 0.5, 1.0, 1.5, and 2.0 kg/s
  3. Compare steady-state amplitudes and time to reach steady state
  4. Graph amplitude vs. damping coefficient

Activity 3: Phase Relationships (5 minutes)

  1. Observe the phase lag indicator at different frequency ratios
  2. Note: Below resonance (nearly in phase), at resonance (90° lag), above resonance (nearly 180° lag)
  3. Connect to energy transfer efficiency

Discussion Questions

  1. Why does the amplitude keep growing at resonance?
  2. What role does damping play in limiting the amplitude?
  3. How does this relate to pushing a child on a swing?
  4. Why did the Tacoma Narrows Bridge collapse? How could engineers prevent similar failures?
  5. How do noise-canceling headphones use the principle of driven oscillations?

Assessment

  • Formative: Observe student predictions before adjusting parameters
  • Summative: Students explain in writing why a wine glass shatters when a singer hits the right note
  • Extension: Calculate the theoretical resonance amplitude using the formula and compare to simulation results

References

  1. Forced Oscillations and Resonance - OpenStax University Physics - Comprehensive textbook treatment of driven oscillators with mathematical derivations

  2. The Tacoma Narrows Bridge Collapse - 1940 - Historical footage demonstrating catastrophic resonance failure in engineering

  3. Resonance in Physics - The Physics Classroom - Accessible introduction to resonance concepts for high school students

  4. Damped and Driven Oscillations - Feynman Lectures on Physics - Richard Feynman's classic explanation of oscillatory systems

  5. p5.js Reference - p5.js Documentation - JavaScript library used to create this interactive simulation