Damped Natural Frequency
Calculate the damped natural frequency of a vibrating system, ω_d = ω_n·√(1 − ζ²), from the undamped natural frequency ω_n and the damping ratio ζ. The result, in the unit of ω_n (rad/s or Hz), is the actual frequency at which an underdamped system oscillates freely after a disturbance — always lower than the undamped natural frequency, since damping slows the oscillation. For small ζ (lightly damped systems), ω_d ≈ ω_n; as ζ → 1 (critical damping), ω_d → 0 and the system stops oscillating. Enter the natural frequency and the damping ratio.
Resultado
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Frequência natural amortecida
Um sistema massa-mola-amortecedor, ao ser perturbado e solto, oscila livremente — mas o amortecimento não só faz a amplitude decair como também desacelera a própria oscilação. A frequência real dessa oscilação amortecida é ω_d = ω_n·√(1 − ζ²), onde ω_n é a frequência natural não amortecida (a que o sistema teria sem atrito) e ζ é a razão de amortecimento (a fração do amortecimento crítico). O fator √(1 − ζ²) é sempre ≤ 1, então a oscilação amortecida é sempre mais lenta que a não amortecida. Para sistemas pouco amortecidos (ζ < 0,1, comum em estruturas metálicas), a diferença é desprezível e ω_d ≈ ω_n. Mas conforme ζ aumenta, ω_d cai: em ζ = 0,6, a frequência amortecida é 80% da natural. No limite do amortecimento crítico (ζ = 1), ω_d chega a zero — o sistema não oscila mais, apenas retorna lentamente ao equilíbrio sem ultrapassá-lo. Acima disso (ζ > 1, superamortecido), o movimento é puramente exponencial. A frequência amortecida é o que se mede experimentalmente no decaimento livre de uma estrutura, e dela, junto com o decremento logarítmico, extrai-se o amortecimento real do sistema. Informe a frequência natural e a razão de amortecimento.
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