Free vibration control for damped system under harmonic loads?

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Dear engineers, I want to find the normalized stiffness for the machine with unbalanced force Ps_s(t)=P0 sin w0t and also the steady-state transmitted force fs_s(t)= f0 sin(w0-phi). and the given parameters are w0*t0=50*pi.

Then I want to find the analytical expression of the phase angle and angular velocity and unbalanced force.

Also in the attachment, I uploaded the problem.

I really appreciate if somebody can refer me to the relevant example or topic can help to solve this problem or even part of that.



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