5 ms·
Ah I see you already wrote a similar comment as me. You are more correct. I assumed the ball would bounce lower and lower, but never constantly on the ground.
by beiller 9y ago
Ah I see you already wrote a similar comment as me. You are more correct. I assumed the ball would bounce lower and lower, but never constantly on the ground.
- deleted 9y ago[deleted]
- tzahola 9y agoIf we put perfect elasticity aside (that is, the coefficient of restitution [0] is < 1) then the ball would bounce back to exponentially decaying heights. However, because of this, the duration of each bounce would also get shorter and shorter in an exponential rate. Now, because the exponential series converges to a finite value, they argue that the ball would bounce infinitely many times in a finite amount of time, after which the ball would be standing still on the ground (the bounce height having converged to 0). [0] https://en.m.wikipedia.org/wiki/Coefficient_of_restitution https://en.m.wikipedia.org/wiki/Coefficient_of_restitution
- beiller 9y agoOkay I guess I see the point is that the bouncing ball converges to a default state, unlike a light switch, which converges to an unknown state. Is it the force of "gravity" which causes this default state, so does the convergence just cancel out all other influences on the system state perhaps?
- tzahola 9y agoThe ball's state can be described by its y coordinate, and it converges to zero. The lightbulb's state can be described by Boolean variable (on/off), but it doesn't converge, just oscillates between on and off with an exponentially increasing frequency. If we have instead used a variable intensity light switch, and turned it like 0%, 100%, 0%, 50%, 0%, 25%, 0%, 12.5% ..., with an exponentially increasing frequency, it would have also converged to the 0% state like the ball did. So the variables that describe the system's state has to converge.