How to input amplitude on a second order transfer function?

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André Rocha 2019-5-18

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https://ww2.mathworks.cn/matlabcentral/answers/462835-how-to-input-amplitude-on-a-second-order-transfer-function

Please, I have a question that I believe it's simple to solve.

I have some samples of readings from an accelerometer (unit: g) and I did a FFT (on MATLAB) on the vector generated from these samples to see its frequency spectrum. Then I have isolated the peaks and located its frequency. OK, now the control theory question. Let's say, to simplify the example, the only peak is 2 g at the frequency of 10 Hz. The accelerometer acquired the samples over a vibration system, so I assume it is undamped oscillating endelessly at a natural frequency of 10 Hz. My transfer function would be:

I multiplied by 2 before raising because it's given in Hz and I have to convert it into rad/s (right?)

I intend to make a PID control (on Simulink) to analyze some parameters, as overshoot, settling time, etc. The REAL question is: how do I "tell" the system that the amplitude of it is 2 g? Is it like a gain that I insert before the transfer function block? Image below: