Building realistic simulation using differential equations [closed]

Question

I am building simulation using differential equations to model the motion of a damped vertical spring-mass system. I wish to use this simulation to extract data. For example, I am trying to find the effect of mass on the damping.

The problem I am facing is every time I run the model, I receive the same numbers. Thus, I cannot run multiple trials. This makes sense because the model is purely iterative. How do I add a bit of randomness to the model to make it more realistic and usable for experimentation?

Answer 1

The answer to the question as asked is “you add randomness to the system parameters and initial conditions”. Some search terms are “uncertainty quantification” and “design of experiments”.

But ... those techniques are used for models where there isn’t a detailed analytic understanding of the end-to-end behavior of the system. They would be wasteful overkill for the system in front of you.