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    Mechanical Vibrations

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    1) A machine tool having a mass of 1000 kg and a moment of inertia J = 300 kg-m2, is supported on elastic supports with stiffness's and locations shown.
    i) Find the natural frequencies of the machine tool.
    ii) What are the corresponding amplitude ratios?

    (There are 2 separate questions in 1 problem).

    Please see attached figure.

    For i ), which one is correct answer:

    (a) 35.63 rad/s, 41.17 rad/s
    (b) 58.70 rad/s, 62.37 rad/s
    (c) 41.17rad/s, 57.82 rad/s
    (d) 70.58 rad/s, 82.37 rad/s

    See attached file for full problem description.

    For ii ), which one is correct answer:

    (a) -2.383, 0.185
    (b) -5.348, 0.056
    (c) -7.242, 0.024

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    Solution Summary

    The solution finds the natural frequencies of the machine tool as well as the corresponding amplitude ratios (see attachment).