Question

A sensitive electrical measurement device needs to operate near heavy equipment that cause the table the device sits on to vibrate vertically. Whenever the vibration happens the measuring device seems to have erratic readings. A thoughtful ISU graduate has the idea to put springs between the device and the table as shown, to reduce the device's vibration. The weight of the instrument is 500 Newtons. An accelerometer is temporarily attached to the table. The acceleration of this base is 6.075 m/s2 at a frequency of 7.2 Hz. Determine the total mounting spring stiffness needed to reduce the vertical displacement of the measuring device by 70% Assuming any damping is very small

Answer 1

Sol Giuen clata weigut WESTON L6=6.035ml2 wo2P 2*6772 4s.238 Bad s Total seduck on 7o1 Tsanomittedd motion -20 O3 2 2 1+ VI-21224 dampin Neg fe cteal o + 1-2 r =9 V

Ke TOY 1- I 3.333 Ke of Peakibiuty of solutin) 2 3333 J24.833 K コ= 2.082 k r T 2 082 Ka us.238 Wn 2.082 2-082 t)94. was Wne 21.7316 Stf Ke 2 .7316 E O V

Ke (21.7816 Ke = 72.268 y 81 る959S ニ Ke- 472.263gxS09 kE- 240 7o.53 N/m Ke- 24.0 KN/m stff ness af mounting Total asei'ng was <pring a1nc ndiwolual Shef ness Ke = 2k = 24.071EN = 12.03 KNm K 24.07 V
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