How do physicists figure out the equations that model physical phenomena?

Question

For example, we have differential equations that model, for example, resonance, vibration, heat transfer, the motion of a spring, etc. How were these equations first calculated and derived, and to such a degree that we can be sure of their accuracy in modeling real life phenomena? What is the process for actually deriving them like?

In: 4

Answer 1

You make observations.

Then you come up with mathematical equations that produce the same results.

Then you continue to make observations and see how the results of your equations compare with real life occurances.