8.6 Friction, resonances, and beats

Source: Ideas from Computational Physics (Landau, Páez, Bordeianu), §8.6. Original wording. Continues 8.5b. Labs: 8.6b.

Viscous friction

Add drag linear in velocity, classify free regimes, and extend the dynamic-form acceleration $f_1$. Pick each equation among lookalikes.

Regime	Condition	Motion
Underdamped	$b < 2m\omega_0$	decaying oscillation
Critical	$b = 2m\omega_0$	fastest non-oscillatory return
Overdamped	$b > 2m\omega_0$	slow creep, no ringing

A harmonic drive $F_0\cos(\omega t)$ produces a steady response peaked near $\omega_0$ when damping is light. Transient + steady terms with nearby frequencies produce beats at $|\omega-\omega_0|/(2\pi)$ (labs: $\omega=2\pi\cdot 1.1$, $\omega_0=2\pi$ ⇒ $0.1$). Nonlinear restoring forces warp the resonance curve once linear friction/drive is under control.

Quiz

Friction, resonance, beats

1 / 4

Critical damping occurs when…

Pick an answer to see if you are right.

Next: 8.6b Friction and resonance labs.