For Students · Coupled Oscillators
Coupled Oscillators for a yo-yo
Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate a yo-yo live below — adjust the inputs and watch it respond, right in your browser.
Coupled OscillatorsLive
normal modes & beating
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Two masses linked by a spring exchange energy. Any motion is a mix of two normal modes: in-phase (slow) and out-of-phase (fast). Their beat produces the sloshing you see.
Data Inspector
Mode 1 (in-phase)0.712 Hz
Mode 2 (out-of-phase)0.955 Hz
Beat frequency0.243 Hz
Governing equation
Reading this result: The beat frequency is set by the coupling: at kc=8 versus k=20, energy fully sloshes from one mass to the other every 2.1 s, and stiffer coupling speeds that exchange up.
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- Yes — this version of "Coupled Oscillators for a yo-yo" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
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