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3 spring shock absorber help

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  1. Feb 13, 2008 #1
    1. The problem statement, all variables and given/known data
    The problem verbatim from the text:
    "One of the winners in an egg-drop contest was a structure in which rubber bands held the egg at the center of it. Attached is a model. Consider the egg to be a particle of mass m and the springs to be linear with spring constants k. consider only a two dimensional version of the winning design as shown in the figure attached. Assume the frame hits the ground on one of the straight sections. Assume small motions (deflection << side-length) and that the springs do not buckle.
    a)What will be the frequency of the vibrations after the impact?
    b) what is the maximum vertical deflection of the egg (relative to its equilibrium position)?


    2. Relevant equations
    f=1/t=2*(pi)*sqrt(k/m)
    x(t)=Asin(wt+phi) A=amplitude

    3. The attempt at a solution
    I've been dwelling on this question for a while and I've been unable to completely solve it (obviously). Using law of cosines, the initial and final lengths of the side springs and deltaX (the change in length of the top spring), I have derived that the length of the side springs after deflection is approximately equal to:
    L'=sqrt(lo^2-lo*x)
    This is assuming that deltaX is extremely small and when squared in the law of cosines, goes to 0.

    In order to find the frequency, I need to find the effective spring constant, because:
    f=1/T=2*(pi)*sqrt(k/m)
    but I dont quite know where to go from here. Did I make an incorrect approach?
    I have not made an attempt at part b
     

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  2. jcsd
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