Lesson Plan

• Describe how a resistive force proportional to velocity modifies the equation of motion for a mass‑spring system.
• Distinguish under‑, critically‑, and over‑damped regimes using the damping ratio.
• Calculate the damped angular frequency and the exponential decay of amplitude.
• Explain the effect of damping on the amplitude and phase of a forced oscillator.
• Predict the resonant frequency and maximum amplitude for lightly damped systems.

• Projector and screen
• Whiteboard and markers
• Mass‑spring‑damper apparatus (spring, mass, dashpot)
• Motion sensor or video‑analysis software
• Student worksheets with derivations and practice problems
• Scientific calculators or graphing apps

Begin with a short video of a bridge swaying in wind to hook interest. Ask students what forces might be reducing the motion and link this to prior knowledge of simple harmonic motion. State that by the end of the lesson they will be able to predict how damping changes the behaviour of both free and driven oscillators.

1. Do‑Now (5'): Quick quiz on undamped SHM equations and natural frequency.
2. Mini‑lecture (10'): Introduce the damping force $F_d=-b\dot{x}$ and derive the damped equation of motion.
3. Concept exploration (12'): Use the mass‑spring‑damper set to demonstrate under‑, critical‑, and over‑damping; students record displacement graphs.
4. Guided practice (10'): Work through calculations of $\zeta$, $\omega_d$, and exponential amplitude decay on the worksheet.
5. Forced oscillations & resonance (10'): Derive the steady‑state solution, discuss amplitude vs. driving frequency, and relate to real‑world examples.
6. Check for understanding (8'): Exit‑ticket where each student writes the condition for critical damping and one practical implication of damping.

Recap the key idea that a resistive force introduces a velocity term that reduces amplitude and shapes resonance behaviour. Collect exit‑tickets and highlight common misconceptions to address next lesson. Assign homework: complete the worksheet problems on calculating damping ratios and sketching resonance curves.