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kurt1288

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I have to derive a transfer function for the following:

A small satellite with a moment of inertia J1 that has a instrument with a moment of inertia J2. The instrument is at the end of a small strut that has a stiffness constant of k and a damping coefficient of b. A torque is applied to the satellite.

I know that the satellite and instrument (and their respective moments of inertia) can be modeled as two masses with mass m1 and m2. The "strut" above is a spring in this case with the same k and b values. The torque described above can be modeled as a force applied to m1 here. x1 and x2 are the displacements of each mass.

I already have the final transfer function but I don't quite know how to derive it:

X(s)/F(s) =(bs+k)/(J1J2s^4+(J1+J2)bs^3+(J1+J2)ks^2 )