I am trying to write a system model for lowering a mass into water. In my system model, I have a mass hanging freely from a spring and damper connected in parallel. I then try to equate the damping coefficient to the drag experienced by the mass. I have provided the system equation below: my'' = mg - by' - ky where by' = 0.5*rho*Cd*A*y'^2 (drag) the full equation is then: my'' = mg - 0.5*rho*Cd*A*y'^2 - ky My questions: 1) Having the spring and damper in parallel creates a second order non-linear differential equation (atleast I think)...which I have no idea howto solve. I have solved both 2nd order linear and 1st order non-linear diff eq but not 2nd order non-linear. Infact my notes said solving them is kind of a crap shoot. I have found examples with the spring and damper in series rather than parallel, but this does not make sense to me as the spring and damping act together to slow the mass. Is my model correct using parallel instead of series between the spring and damper? 2) If so, is it ok to equate the damping force to the drag force inorder to find a damping coefficient? Any and all help is greatly appreciated.