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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).

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