Differential Equations B — Oscillation & Damping
Part 2 of 2. The harmonic oscillator y″ = −ω²·y, natural frequency √(k/m), and damped oscillation — decay enveloping a wave.
Part 2 of 2. In part A the first derivative gave decay. Let the second derivative into the equation and the behaviour changes completely — things start to oscillate.
- 01 The harmonic oscillator — y″ = −ω²·y ELI5: when a thing's acceleration (second derivative) points back toward home in proportion to how far it has strayed, it can't settle — it swings.…
- 02 Damping — oscillation meets decay ELI5: add friction and the two stories from this track combine: the exponential decay of part A becomes an envelope that slowly strangles the oscillation. The…
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