GATE 2018 ME (ME1) – Question 50
A 200 kg machine rests on two mounts, each of stiffness 10 kN/m. Applied force is $F(t)=50\cos5t$ N. Assume only vertical translation. Dynamic force amplitude transmitted from each mount, to two decimals, is ______ N.
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Correct answer: 33.00 to 33.50
Explanation
Parallel mounts give total stiffness 20000 N/m. Undamped displacement amplitude is $X=50/|20000-200(5^2)|=1/300$ m. Each mount transmits $kX=10000/300=33.33$ N dynamic amplitude, excluding the static weight share.