Just to clarify: In order to get the object to its rest position, we want the force to decrease as we reach the rest position. However, with large time steps we are essentially overshooting as we get close to the rest position leading to a pendulum type of behavior?

Interesting to see an explanation that forward Euler is deterministically unstable for oscillating systems no matter how small you make the timestep! Makes a lot of sense but I had never really thought about why. Thanks!

I am wondering if there is a formal definition of stability.