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