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What happens to the frequency of a swing as its oscillations die down from large amplitude to small ?
The frequency of the damped oscillator is,wʹ = √k/m – (b/2m)2The greater is the damping constant b, the more quickly the amplitude of the oscillation dies out. When damping is present, the oscillation frequency is smaller (the period is larger). That is, damping slows down the motion, as we might expect. If the damping constant b = 0 (no damping), then wʹ = √k/m, which is simply the angular frequency w of the undamped motion.
The greater is the damping constant b, the more quickly the amplitude of the oscillation dies out. When damping is present, the oscillation frequency is smaller (the period is larger). That is, damping slows down the motion, as we might expect. If the damping constant b = 0 (no damping), then wʹ = √k/m, which is simply the angular frequency w of the undamped motion. 2The frequency of the damped oscillator is,wʹ = √k/m – (b/2m)
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