Calculation of Stationary Solution of Forced Oscillation.

Keyword

Stationary Solution,Forced Oscillation,Differential equation,Attenuation factor per unit mass,Frequency for No attenuation,Forced frequency,Forced amplitude per unit mass,Resonance frequency for amplitude of displacement,Impedance per unit mass.

Reference

[1]:Graham Woan著・堤正義訳:『ケンブリッジ物理公式ハンドブック』,共立出版,pp.76,2007.

Remarks

・Making above Equation Image is powered by CODECOGS.
・LaTex: x=Ae^{i\left ( \omega _{f}t-\phi \right )}
・LaTex: A=F_{0}\left [ \left (\omega _{0}^{2} -\omega _{f} ^{2}\right )^{2}+\left ( 2\gamma \omega _{f}\right )^{2} \right ]^{-\frac{1}{2}}
・LaTex: \tan\phi =\frac{2\gamma \omega _{f}}{\omega _{0}^{2}-\omega _{f}^{2}}
・LaTex: \frac{d^{2}x}{dt^{2}}+2\gamma \frac{dx}{dt}+\omega_{0}^{2}x=F_{0}e^{i\omega _{f}t}

History

・2010/03/24:Partial modification about calculation process.
・2010/03/23:Upload.