Find out, under what conditions occurs and is maintained for some time oscillatory motion.

The first condition, necessary for the occurrence of oscillations, is the presence of a material point of excess energy (kinetic or potential) compared with its energy in the stable equilibrium position.

The second condition you can install, tracing the movement of cargo 3 in figure. 24.1. In position b for the cargo 3 the force of elasticity F₁, directed to the equilibrium position of the cargo. Under the influence of this power load is shifted to the equilibrium position with gradually increasing speed υ, and the force F₁ decreases and disappears, when the cargo gets to that position (rice. 24.1, in). The speed of the goods at the time of maximum largest, and cargo, skipping through the equilibrium position, continues to move to the right. Thus there is a force of elasticity F₂, which inhibits the movement of cargo 3 and stops it (rice. 24.1, g). Power F₂ this position has a maximum value; under the action of this force cargo 3 starts to move left. In the equilibrium position (rice. 24.1, d) power F₂ disappears, and the load velocity reaches the highest value, therefore, cargo continues to move left, until you occupy the position b in figure. 24.1. Further, this entire process is repeated again in the same order.

Thus, fluctuations of cargo 3 occur due to the action of the force F and the load inertia. Force, applied to the material point, always directed to the position of stable equilibrium points, call return force. In stable equilibrium position the restoring force is zero and increases with distance of points from this position.

So, the second condition, necessary for the emergence and continuation of oscillations of a material point, is the action on a material point restoring force. Recall, that power is always there, when a body is inferred from the equilibrium position.

In the ideal case, in the absence of friction and resistance of environment, full mechanical energy of an oscillating point remains constant, because in the process of such variations, only transition of kinetic energy into potential energy and back. This oscillation should continue indefinitely.If oscillations of a material point occurs in the presence of friction and resistance of environment, the total energy of a material point gradually decreases, the amplitude of oscillations decreases and after a while the point stops at the position of stable equilibrium.

There are cases, when the energy loss of a material point is so great, what if external force deflects this point from the equilibrium position, it loses all its excess energy when returning to the equilibrium position. In this case, oscillations will not work. So, the third condition, necessary for the emergence and continuation of oscillations, the following: excess energy, received a material point the displacement from the equilibrium position, should not be spent on overcoming the resistance when returning to that position.