An apparatus known as a centrifuge is commonly used to separate solutions of different chemical compositions. It operates by rotating at high speeds to separate substances of different densities.

Fig. P3.1 Centrifuge model with a single vial

(a) If a single vial with a mass of \(0.2 \mathrm{~kg}\) is placed in the centrifuge (see Fig. P3.1) at a distance of \(20 \mathrm{~mm}\) from the rotating axis, determine the magnitude of the resulting vibration, \(X\) (in \(\mathrm{mm}\) ), of the single degree of freedom centrifuge structure. The rotating speed is \(200 \mathrm{rpm}\).
(b) Determine the magnitude of the forcing function (in \(\mathrm{N}\) ) due to the single \(0.2 \mathrm{~kg}\) vial rotating at \(200 \mathrm{rpm}\).

Transcribed Image Text:

k = 1000 N/m c = 50 N-s/m x(t) k 20 mm k Centrifuge mass is 2 kg. Single vial with m = 0.2 kg