Damped Harmonic Oscillation | AP Physics | ShowMeClass

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Damped Harmonic Oscillator

AP Physics 1 · Unit 6: SHM

Key Objectives

Observe the exact mathematical shift between Underdamped, Critically Damped, and Overdamped regimes.

Compare the physical visual of a fluid tank getting more viscous with the theoretical envelope.

D3 Graph: See the $e^{-\gamma t}$ decay envelope physically wrapping the oscillating signal.

Differential Equation

Where $\omega_0 = \sqrt{k/m}$ and $\gamma = b/(2m)$

Underdamped ($\gamma < \omega_0$)

Damping ($b$) Decay Envelope Differential Eq

Regime Status

UNDERDAMPED

Time ($t$)

0.00 s

Displacement ($x$) vs Time ($t$)

⚙️ Oscillator Settings

Spring Constant ($k$) 20.0 N/m

Mass ($m$) 2.0 kg

🌊 Environment Settings

Viscous Damping ($b$) 1.5 N·s/m

Theoretical Analysis

          Natural Freq ($\omega_0$): 0.0 rad/s

          Damping Ratio ($\gamma$): 0.0 s⁻¹

          Crit. Damping ($b_c$): 0.0 N·s/m