some insights on physics of this simulation

[nort3x]

physics student here

use velocity verlet method to update velocity and position
it's more efficient than RK4 and it's stable (it doesn't diverge like euler method)

and the wiggly thing is expected and it's because of conservation of energy as ball drops and it gains velocity (kinetic energy) due collision the kinetic energy is transferred to your spring-mass system energy and it wiggles wildly (it's actually temperature) to cancel it out define some dispersion of energy just add a damping factor to your hook law
F = ma = -k* x - d*v
and it should work.