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2d oscillators

  1. Nov 8, 2004 #1
    hi, I was going through my homework and i came to a problem that i cant seem to get.
    Consider the mass attached to four identical spring. Each spring has the force constant k and unstreched length L_0, and the length of each spring when the mass is at the origin is a(not necessarily the same as L_0). When the mass is displaced a small distance to the point (x,y), show that its potentail energy has the form 1/2*K_prime*r^2 appropriate to an isotropic harmonic oscillator. What is the constant K_prime in terms of k? Give an expression for the corresponding force.

    I started this problem by calculating the force on each spring in the x direction and got
    F_1(x)= -k(x+a)+(k*L_0(x+a)/sqrt((x+a)^2+y^2))
    F_2(x)= -kx + (k*L_0*x/sqrt(x^2+(y-a)^2))
    F_3(x)= -k(x-a) + (k*L_0*(x-a)/sqrt((x-a)^2+y^2))
    F_4(x)= -kx + (k*L_0*x/sqrt(x^2+(y+a)^2))

    i tried to simplify these forces but cant seem to get any where with it, i think the fact that the displacement from (x,y) has something to do with it, but im not sure how to implement that into the problem.

    anyone have any ideas?

  2. jcsd
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