Second Order System Governing Equationsfrom "Introduction to Mechatronics and Measurement Systems" (2nd edition)by Alciatore and Histanddifferential equation:natural frequency:critical damping constant:damping ratio(“zeta”):damped natural frequency:Frequency Responseforcing function:steady state frequency response:amplitude ratio:phase angle:md2xdt2--------bdxdt------kx++ Fextt()=ωnkm----=bc2 km 2mωn==ζbbc-----b2 km--------------==ωdωn1 ζ2–=Fextt() Foωt()sin=xt() Xoωt φ+()sin=XoFok⁄------------11ωωn------2–24ζ2ωωn------2+12⁄----------------------------------------------------------------------------=φ tan1–2ζωnω------ωωn------–-------------------–=Second Order System Frequency Response from “Introduction to Mechatronics and Measurement Systems” (2nd edition) by Alciatore and Histand 0.010.1110Amplitude Ratio (kX / F) oo0.01 0.1 1ζ = 0.010.3(ω / ω )nFrequency Ratio0.7072510 -180-135-90-4500Phase Angle (°)123ζ = 0.010.3(ω / ωn)Frequency
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