Why do oscillations occur around the equilibrium point?

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In summary, the conversation discusses oscillations and how they can be explained using the laws of conservation of energy and the relationship between force and displacement. The speaker also mentions the concept of equilibrum points and how they relate to the distance from the center of the Earth. They also mention the release of energy and the creation of a singularity as a result of gravity acting on matter. The speaker also expresses their love for the forum and questions why there are no replies to their posts.
  • #1


Around equilibrum point!

i chacked my books on periodical/oscilatory motion and this is what i found:
this is at best description how not explanation why oscilations take plase.by the way here I'm going to show that it's not quite right.


oscilations could be explained with only two laws
the news is that the bold are vectors.
F=the vector of the force positioned on y-axes
R=the distance from the object to the equilibrum point positioned on x-axes
E=energy positioned on z-axes
the first (1) is conservation of energy.
the second (2) is my substitution for the invalid Newton the 2nd.
the second (2) also states that the force and the displacement have same direction or the force is the reason for the contineuos displacement (never being at rest).here actually all the vectors are constant by norm/magnitude except the fact that E is also constant in direction while F and R are rotating around E.draw it in 3d.
in a case of "tunnel thru earth" scenario we project every vector on the y-axes (parallel with the force) and then:
this means that at the extreme distance from the equilibrum point the force is zero and at the equilibrum point the force is extreme.on the other hand we are sure that at extreme height from the center of the Earth in that scenario the force is extreme.that's why the equilibrum points are the most distant point from the centar of the earth.
while I'm here i'd like to stress that:
when the matter gets densed by the gravity pull, in order to make certain densed state a state of equilibrum it will have to release some energy (preferably thru an explosion) and what's more to it; an point of singularity creation takes release or infinite amount of energy.if no energy is being released then the matter will oscilate around the equilibrum point/state.

Thank you very much.
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  • #2
why there are no replies?
no one got any thing to say?
am i not clear enough?

assume you have an object hanging on a sping.when you are pull it down for x distance from the equilibrum point you can say that at the moment of releave the distance from the eqilubrum is max but then the force has to be zero.otherwise you can say that the force is max but then the distance has to be zero.
actually they are both right if you know where you project them.

if you project the F(orce) and the D(istance) on F direction then:

if you project the F(orce) and the D(istance) on D direction then:
Dy=Dmaxcos(fi2) where fi2=-fi1

and then:

there is no doubt that
Energy vector = Force vector x Distance vector.

the second law just gives the perpetual push.

1. Why do oscillations occur around the equilibrium point?

Oscillations occur around the equilibrium point due to the presence of a restoring force. This force acts to bring the system back to its equilibrium position whenever it is displaced. As the system moves away from the equilibrium point, the restoring force increases, causing the system to reverse its direction and move back towards equilibrium. This back-and-forth movement results in oscillations.

2. What factors affect the amplitude of oscillations?

The amplitude of oscillations is determined by the initial displacement from equilibrium, the strength of the restoring force, and the amount of energy in the system. A larger initial displacement or stronger restoring force will result in larger oscillations, while a higher energy level will cause the oscillations to gradually decrease in amplitude over time.

3. How does damping affect oscillations?

Damping is the process of reducing the amplitude of oscillations over time. It occurs when there is a resistive force acting on the system, such as air resistance or friction. The amount of damping present can significantly affect the behavior of oscillations. Underdamped systems will continue to oscillate, but with gradually decreasing amplitude. Critically damped systems will reach equilibrium quickly without any oscillation, while overdamped systems will take longer to reach equilibrium and will also not exhibit oscillatory behavior.

4. Can oscillations occur without an external force?

In most cases, oscillations require an external force to initiate and maintain them. However, there are some systems that can exhibit oscillatory behavior without any external force, such as a simple pendulum. These systems rely on the force of gravity and the potential energy of the system to create oscillations.

5. Why is the equilibrium point important in oscillatory systems?

The equilibrium point is the stable point where the forces acting on the system are balanced. It is important because it serves as the reference point for the system's motion. Without an equilibrium point, the system would not exhibit oscillatory behavior as there would be no restoring force to bring it back to a stable state. The distance from the equilibrium point also determines the amplitude of oscillations.

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