
Denote by G(iω) the frequency response of Eq. (i), that is, the ratio of the steady-state response to the harmonic input u(t)=Aeiωt. The transmissibility TR of the platform mounting system is then defined to be the corresponding gain function, TR=|G(iω)|. Show that TR can be expressed as
TR=√1+(2ζωω0)2√[1−(ωω0)2]2+[2ζωω0]2.
Eq. (i) y″+2ζω0y′+ω20y=2ζω0u′+ω20u.

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