I understand the equation of a damped mass system (spring plus dashpot) when one end is fixed to a wall as is described in most textbooks. However, I need an equation of the more interesting case where two free floating masses are connected by a single axis spring and a dashpot. How would I model the motion of a seat that is attached to a boat by a damping device? If I can measure accelerations in three axes at the base of the damping device, how do I describe the forced vertical motion of the seat that sits on top of the damper? What is the total mass that I insert into the equation, the mass of the seat plus the mass of the damper or the mass of the seat plus the mass of the damper plus the mass of the boat?
Additionally, what is the best way to model the flexibility of the other two axes of the damper system (the almost rigid axes where the damping device bends just a little)? I have heard of the 'hysteretic' model of a beam, but I 1) do not know how to properly force it in this case, and 2) I do not know how to interpret the complex results in a meaningful way. Do I just drop the complex part or does the magnitude represent the deflection? Can I separate each axes of motion or are coupled equations necessary?
Thanks for you help!
