Parameters of a Damped Oscillator

I want to estimate the parameters for a damped oscillator from an observed output (assuming the system acts like a damped oscillator). The attached evaluates the solution for a damped oscillator with zero initial conditions and a forcing function that ramps up to a unit value then ramps down to zero. And gives an example for assumed damping, etc. But I am interested in the inverse problem: Given only the output, how can I estimate or infer the parameters of the oscillator knowing only that the forcing function is as given? Can someone put me on to a systematic way to do this?