Natural Frequency from Static Deflection
Calculate a system's natural frequency from its static deflection, f_n = (1 ÷ 2π)·√(g ÷ δ), where δ is the static deflection caused by self-weight and g the gravitational acceleration (9.81 m/s²). The result, in Hz, is a practical and elegant way to estimate the natural frequency without separately knowing mass and stiffness — you just measure how much the system sags under its own weight. Larger deflections (more flexible systems) give lower natural frequencies, desirable in vibration isolators. It is widely used in spring and mount design. Enter the static deflection (in metres).
Resultado
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Frequência natural pela deflexão estática
Existe um atalho elegante para estimar a frequência natural de um sistema massa-mola sem precisar conhecer separadamente a massa e a rigidez: basta medir o quanto o sistema afunda sob o próprio peso. Essa é a deflexão estática δ, e a frequência natural sai de f_n = (1 ÷ 2π)·√(g ÷ δ), com g = 9,81 m/s². A fórmula vem de uma simplificação bonita: a frequência natural é (1/2π)√(k/m); como o peso mg deforma a mola em δ = mg/k, a razão k/m é igual a g/δ — a massa some da equação! Tudo o que importa é quanto o sistema cede sob o peso. A relação é inversa e muito visual: sistemas flexíveis (deflexão grande) têm frequência natural baixa; sistemas rígidos (deflexão pequena) têm frequência alta. Uma deflexão de 1 cm corresponde a uma frequência natural de ~5 Hz; de 1 mm, ~16 Hz; de 10 cm, ~1,6 Hz. Essa é a base do projeto prático de isoladores de vibração: para isolar bem uma máquina, o isolador precisa ter frequência natural bem abaixo da frequência de excitação — ou seja, precisa ser macio o suficiente para afundar bastante sob a carga. Catálogos de coxins e molas costumam listar diretamente a deflexão estática justamente porque ela informa, num só número, a frequência natural que aquele isolador proporcionará sob carga. É também usada para checagem rápida de fundações de máquinas e estruturas. Informe a deflexão estática em metros.
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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.
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Belt Span Natural Frequency
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.