Calculating steady state response from displacement variance OR finding value of integrand of definite integration from its solution

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I am working on optimization of Tuned Mass Damper Inerter (a device used in earthquake engineering). I have calculated variance of displacement and want to calculate steasy state responce using its equation.
Actually it is a mathematics related problem which i want to solve with use of MATLAB. definite integration of response over 0 to inf. is Variance. So i want to go in reverse direction. i.e. want to find response from variance. What should the approach? Please check the attached image.
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Komal Rajana
Komal Rajana 2021 年 6 月 7 日
Hello, the time-domain response can be obtained via the transfer-function (H(w)) in a simple simulink model.

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