4 thoughts on “3.22”

  1. Howdy sir,

    I'm not exactly sure why you used J(r). It seems like it is a base excitation function, so why/how did you branch the two. Basically, I see that for Yop = G(r) * A and then G(r) is this huge equation that has the [1+4(z^2)(r^2)]^.5 and not the one with r^2 on top.
    So where I'm confused at is how you branched the amplitude formula for a rotating imbalance to the transfer function of a base excitation. Sorry if this is a dumb question, but I don't quite see it. Thanks for your help sir.



    1. Hi Bailey,

      Notice that for base excitation problems we are seeking to know how the body moves relative to a fixed-point. In this problem we are asked to describe the motion of the body relative to the base! (Notice that the roller that accepts the marking is attached to the base while the marker is attached to the moving mass.) There are many cases when an engineer might want to know this relative displacement, and the appropriate amplitude ratio is well studied. It is uncanny that the amplitude ratio happens to be the same as systems with rotating imbalances, but you know... physics.

      Table 3.2 "Forced-Excitation Results where r = \frac{\omega}{\omega_n}" in the textbook (at least it was called Table 3.2 in the tenth edition; it is on page 75) has a row labeled "Relative deflection with base excitation". The symbol used to denote this relative deflection is \Delta. Many of the equation sheets floating around omit this row (perhaps Dr Childs rarely gave problems of this sort), but the textbook documents the relation and its derivation.

      All the best,

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