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Around equilibrum point

  1. Apr 5, 2003 #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 gonna 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.
  2. jcsd
  3. Apr 7, 2003 #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.
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