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Oscillation of nonrelativistic Strings

  1. Dec 10, 2014 #1
    1. The problem statement, all variables and given/known data
    Calculate the horizontal force dFhorizontal of a string .Show that for small oscillations this force is much smaller than the vertical force dFvertical responsible for the transverse oscillations.
    [I apolagize for the way the equations are written]

    2. Relevant equations

    dFvertical=T0dy/dx*-T0dy/dx*1
    *for x+dx *1 for x

    T0(d^2 y/d^2 x)dx=(μ0dx)d^2 y/dt^2

    3. The attempt at a solution

    1.substituting y+dy and y for x+dx and x; substituting dx/dy for dy/dx for horizontal oscillation.
    dFhorizontal=T0dx/dy*-T0dx/dy*1
    *for y+dy *1 for y
    2.exchanging d^2 y/ dx^2 with d^2 x/dy^2 and dx with dy...

    T0 (d^2 x/dy^2) dy= (μ0dx)(d^2 x/dt^2)

    This is as far as I get. I dont know how to show that the horizontal force is smaller than the vertical force for small oscillations.

    Thanks for any clarifications and corrections.
     
    Last edited: Dec 10, 2014
  2. jcsd
  3. Dec 12, 2014 #2

    Orodruin

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    I would instead express the forces (both horizontal and verical) in terms of y(x) and its derivatives wrt x. You can then compare the two with the assumption of small oscillations giving you dy/dx << 1.
     
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