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How to find the transfer function (frequency response function) given the EOM

  1. Sep 30, 2011 #1
    for a given spring/damper system the equation of motion is:

    [PLAIN]http://img600.imageshack.us/img600/2140/equation1.png [Broken]

    where x is the displacement of a mass from a fixed point
    d is a damping constant
    L1 and L2 constant lengths
    k1 and k2 are 2 spring constants
    and Y(t) is a harmonic input fuction

    How can i find the transfer function of this system?
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Oct 1, 2011 #2

    You need to find x(t)/y(t). For this you can assume a harmonic forcing function, for example:

    Y(t) = Y0 sin(wt)

    and corresponding displacement function:

    X(t) = X0 sin(wt-phi), where phi is the phase lag between applied force and resultant displacement.

    You input these equations in your equation and solve (considering differential xdot and xdotdot). After substitution, replace X0sin(wt-phi) term with x(t).

    Then you will get left side of the equation in terms of x(t). x/y gives you FRF.

    Being a single dof, it should be easier for you to calculate by hand.

    You can refer any standard vibrations book for this.

    Best wishes
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