A certain machine of mass 8 kg with supports has an

Chapter , Problem 13.20

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A certain machine of mass 8 kg with supports has an experimentally determined natural frequency of 6 Hz. It will be subjected to a rotating unbalance force with an amplitude of 50 N and a frequency of 4 Hz.

a. Design a vibration absorber for this machine. The available clearance for the absorber's motion is 0.1 m.

b. Let \(x_1\) be the vertical displacement of the machine. The amplitude of the rotating unbalance force is \(m_u \in \omega^2\). Plot \(X_1 / m_u \epsilon\) versus the frequency \(\omega\), and use the plot to discuss the sensitivity of the absorber to changes in the frequency \(\omega\).

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