Pendulum Equilibrium: Can It Pass Balance Point Twice?

[walter1998]

Consider a pendulum in it's balance point hanging from ceiling. It can swing in all the directions in the space. The pendulum can only swing in a sphere(the string can't bend). Now, is it possible to release the pendulum in a particular height and with a initial condition that in the first go(the same height as the first place) it doesn't pass the balance point but in the return it does? (don't count air or friction)
If it is possible what initial conditions and height(s) are required?
If not why?

 

[mfb]

What do you think?

 

[walter1998]

What do you think?

I think it is possible but i cannot prove it; I'd be glad if you could guide me or more glad if you solve it.

 

[mfb]

I think it is possible

In which way?

Also, how would the time-reversed process look like?

Spoiler

What do you know about angular momentum?

 

[PJC01]

I would approach this question by first considering the basic principles of pendulum motion. A pendulum's equilibrium position is at its lowest point, where it has the most potential energy. As it swings back and forth, it continuously converts this potential energy into kinetic energy, reaching its maximum velocity at the bottom of each swing. As the pendulum reaches its highest point on the other side, it has lost all of its kinetic energy and is again at its equilibrium position.

Based on these principles, it is not possible for a pendulum to pass its equilibrium point twice in a single swing without the influence of external forces such as air resistance or friction. This is because the pendulum's energy is continuously being converted from potential to kinetic and back again, resulting in it always returning to its equilibrium position.

In order for the pendulum to pass its equilibrium point twice in a single swing, there would need to be a source of additional energy to overcome the pendulum's natural motion. One possible way to achieve this could be by introducing a second pendulum that is synchronized with the first, providing a boost of energy at the appropriate time to allow the first pendulum to pass its equilibrium point twice.

In terms of initial conditions and height, the specifics would depend on the exact setup and design of the pendulum system. However, in general, the initial height and velocity of the pendulum would need to be carefully calculated and controlled in order to achieve the desired result. Any deviation from these initial conditions could result in the pendulum behaving in a different manner.

In conclusion, based on the principles of pendulum motion, it is not possible for a pendulum to pass its equilibrium point twice in a single swing without external forces. However, with careful design and control, it may be possible to achieve this result through the use of synchronized pendulum systems.