Here is what I am reffering to when I say approximation,
It is known that a swinging pendulum satisfies (am I right?):
What physcisits do is approximate the solution for small t that is sin t=t then,
This is a linear differencial equation and it becomes simpler.
However, a mathematicians would not be satisfied with such an approach because it is not exact that t=sin t
To add I think there is something called "linearizing" in applied math to simplify the functions but mathematicians do not deal with such problems. Even more they are useless.