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# Answer to Question #150757 in Mechanical Engineering for Thomas yau

Question #150757
A 110 kg machine is mounted on an elastic foundation of stiffness 2 x106 When operating at 150 rad, the machine is subject to a harmonic force of magnitude 1500 N. The steady-state amplitude of the machine is measured as 1.9 mm. What is the damping ratio of the foundation?
1
2020-12-22T05:05:59-0500

"A=\\frac{F_0\/k}{\\sqrt{[1-(\\frac{\\omega}{\\omega_n})^2]^2+[\\frac{2\\xi\\omega}{\\omega_n}]^2}}"

"1.9*10^{-3}=\\frac{1500\/2*10^6}{\\sqrt{[1-(\\frac{\\omega}{\\omega_n})^2]^2+[\\frac{2\\xi\\omega}{\\omega_n}]^2}}"

"{[1-(\\frac{\\omega}{\\omega_n})^2]^2+[\\frac{2\\xi\\omega}{\\omega_n}]^2}=\\frac{1500}{2*10^6*1.9*10^{-3}}=\\frac{15}{38}"

"[2.2248*\\xi]^2=0.39473-0.05640"

"2.2248*\\xi=\\sqrt{0.33834}"

"\\xi=0.2614"

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