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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Logarithmic decrement ： ウィキペディア英語版 Logarithmic decrement Logarithmic decrement, $\backslash delta$, is used to find the damping ratio of an underdamped system in the time domain. The logarithmic decrement is the natural log of the ratio of the amplitudes of any two successive peaks: : $\backslash delta\; =\; \backslash frac\; \backslash ln\; \backslash frac,$ where x(t) is the amplitude at time t and x(t+nT) is the amplitude of the peak ''n'' periods away, where ''n'' is any integer number of successive, positive peaks. The damping ratio is then found from the logarithmic decrement: : $\backslash zeta\; =\; \backslash frac)^2\}\}.$ Thus logarithmic decrement also permits to evaluate the Q factor of the system: : $Q\; =\; \backslash frac,$ : $Q\; =\; \backslash frac\; \backslash sqrt\})^2\}.$ The damping ratio can then be used to find the natural frequency ''ω''''n'' of vibration of the system from the damped natural frequency ''ω''''d'''':'' : $\backslash omega\_d\; =\; \backslash frac,$ : $\backslash omega\_n\; =\; \backslash frac\{\backslash sqrt\{1\; -\; \backslash zeta^2\}\},$ where ''T,'' the period of the waveform, is the time between two successive amplitude peaks of the underdamped system. The method of logarithmic decrement becomes less and less precise as the damping ratio increases past about 0.5; it does not apply at all for a damping ratio greater than 1.0 because the system is overdamped. ==Simplified Variation== The damping ratio can be found for any two adjacent peaks. This method is used when n=1 and is derived from the general method above: : $\backslash zeta\; =\; \backslash frac\})^2\},$ where ''x''''0'' and ''x''''1'' are any two successive peaks. And for system (not too close to the critically damped regime, where $\backslash zeta\; =\; 1$). : $\backslash zeta\; =\; \backslash frac.$ 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Logarithmic decrement」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.