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Oscillation problem

  1. Oct 31, 2014 #1
    1. The problem statement, all variables and given/known data
    mass "m" object is located near the origin of the coordinate system. External force was exerted on the object depending on the coordinate by the formula of Fx=-4*sin(3*pi*x). Find the short oscillation period, and the potential energy depending on the coordinate.

    2. Relevant equations
    F=ma

    3. The attempt at a solution
    I am not really sure what is the short oscillation period... but
    since there is only 1 force:
    F=Fx=ma
    -4sin(3*pi*x)=m*(d^2*x)/dt^2

    and assuming that the object will move very little (because it's said to be SHORT osccilation period ?)
    sin(3*pi*x) is approximately 3*pi*x .
    and since
    2*x=(d^2*x)/dt^2 is the formula of the harmonic oscillation :
    we find ω=12*pi/m
    and the T=2*pi*√(m/(12*pi)) ?

    and also assuming that in SHORT oscillation :
    it is almost like a spring :
    F=-12*pi*x=-kx
    k=12*pi

    potential energy is Ep= k*x^2/2=6*pi*x^2 ???
     
  2. jcsd
  3. Oct 31, 2014 #2

    vela

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    This is fine.

    I think the problem is looking for the potential corresponding to the original force, not the approximation.
     
  4. Oct 31, 2014 #3
    Thank You for your reply, Vela

    umm...then, i have no other ideas other than using FORCE to solve this problem :PP which is :
    F=-kx
    Fx=F=-4*sin(3*pi*x)=-kx from this
    we find k=4*sin(3*pi*x)/x
    so Ep=kx^2/2=2*sin(3*pi*x)*x ???

    is it right ? :P

    Thanks
     
  5. Oct 31, 2014 #4

    vela

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    How are potential energy and force related in general?
     
  6. Oct 31, 2014 #5
    Maybe the work done by force is divided into object's konetik and potential energy ?
     
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