Pendulum

When one talks about fluctuations, one usually remembers a pendulum. Why does he hesitate? And what are its fluctuations remarkable?

If the load on the suspension is considered a small heavy point (such a pendulum is called mathematical), then the period T of oscillations is directly proportional to the square root of the length of the pendulum. If these fluctuations do not occur on the surface of Earth, and on Moon for example, or on a high mountain, or deep mine, then the acceleration of gravity differs from that to which we are accustomed: g = 9,81 m/s². And then it is important for us to know that the period of oscillations is inversely proportional to the square root of the acceleration due to gravity.

Interestingly, if the pendulum on the Earth (at the ocean level) has a period of 1 second, then what will be its period on the Moon, where the acceleration of gravity is 1,6 m/s²? Since this is 6,13 times smaller than on Earth, the oscillations will occur 2,47 times slower, and the period will be 2,47 times greater, or 2,47 seconds. Hence, the pendulum on the Moon will be lagging behind.

On the contrary, on the giant planets, where the acceleration of gravity is enormous, this pendulum will be in a great hurry.

On Earth, this can also happen. For example, on high mountains the acceleration of gravity is slightly less than at the level of the ocean. There the pendulum will oscillate more slowly, but the oscillation period of the pendulum will react even less, since it depends on the square root of the gravity acceleration relations. This gap will practically not be noticed.

With the descent into the shaft, the pendulum will again hurry due to a certain increase in the acceleration of gravity, but only to a certain depth, which is difficult to pinpoint. After it, because of the decrease in the acceleration of gravity, the pendulum will again fall behind, well, and in the center of the Earth, if we get there, it will stop altogether. For there weightlessness and the acceleration of gravity is zero.

It is interesting that in the same way the pendulum will stop in a falling elevator and in the satellite, flying around the Earth with idle engines, where, as is known, also zero gravity.

But if we create artificial gravity by rotating the satellite, for example, around its axis, then the pendulum will work again, but only if the oscillations of the pendulum occur in the plane of rotation of the satellite.