Damped & Driven Oscillations – AP Physics C | ShowMeClass

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Damped & Driven Oscillations

AP Physics C · Unit 6: Oscillations

Learning Objectives

Solve the damped oscillator ODE

Classify under-, critically, & over-damped motion

Understand resonance in driven oscillators

Relate Q factor to sharpness of resonance

Key Equations

Damping Regimes

Under-damped (γ < ω₀): oscillates with decaying amplitude

Critically damped (γ = ω₀): fastest return, no oscillation

Over-damped (γ > ω₀): slow exponential return

Graph Colors

x(t) — Displacement

v(t) — Velocity

Envelope ±A·e^(−γt)

Driving force

DampingResonanceSHMAP Physics C

t =—

x =—

v =—

E =—

x(t)

v(t)

Phase

Energy

Mode

ω₀ = √(k/m) (rad/s) 5.0

γ (damping, s⁻¹) 0.5

x₀ (m) 1.0

v₀ (m/s) 0

F₀/m (drive amp, m/s²) 5

ω_d (drive freq, rad/s) 5.0

Duration (s) 10

Speed 1×

Oscillation Analysis

📝 Quick Quiz▼

1. Critical damping occurs when γ equals:

ω₀/2 ω₀ 2ω₀ ω₀²

2. Resonance in a driven oscillator occurs when ω_d ≈:

ω₀ 2ω₀ γ ω₀/γ

3. In an under-damped system, the amplitude decays as:

e^(−γt) 1/t e^(−γ²t) t·e^(−γt)