Subject 23 · Oscillations

Oscillations

Start with the one condition that defines simple harmonic motion, follow the energy as it sloshes between kinetic and potential, then let the real world in: damping that drains the swing, resonance that feeds it, and the standing waves that music is made of. Every subsection includes a responsive interactive model.

SWINGωRETURN

a = −ω²xSimple Harmonic Motion

The defining condition a = −ω²x, restoring forces, and the periods of springs and pendulums.

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E(T) = ½mω²A²Energy in SHM

Kinetic and potential energy trade places under one constant total, ½mω²A².

→03

A(t) = A₀e^(−γt)Damped Oscillations

Light, critical, and heavy damping; exponential decay and the Q factor.

→04

f(drive) ≈ f₀Forced Oscillations & Resonance

Drive at the natural frequency and small pushes build huge amplitudes — for better or worse.

→05

fₙ = nv/2LStanding Waves

Counter-propagating waves superpose into nodes, antinodes, and the harmonics of strings and pipes.

→06

x = A sin(ωt + φ)Oscillations Calculus

Solve d²x/dt² = −ω²x outright, differentiate for v and a, and read the damped solution.

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Free game · f(drive) ≈ f₀Resonance Rider

Play free, no account needed: pump the swing at the right rhythm and ride the resonance curve. Push in phase and the amplitude climbs; push against the return and you fight your own swing — and the heavily damped levels show you exactly how narrow resonance really is. Five levels.

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Members · classroom mode, full screenPresent this chapter

Pick any Oscillations lesson and project it. Each deck is built from that lesson’s own words — the big idea, the definition, one formula at a time, the misconception, the quick check, and the worked examples — revealed a step at a time with the arrow keys.

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