The vibration table shown in Fig. 1.121 is used to test certain electronic components for vibration. It consists of two identical mating gears \(G_{1}\) and \(G_{2}\) that rotate about the axes \(O_{1}\) and \(O_{2}\) attached to the frame \(F\). Two equal masses, \(m\) each, are placed symmetrically about the middle vertical axis as shown in Fig. 1.121. During rotation, an unbalanced vertical force of magnitude \(P=2 m \omega^{2} r \sin \theta\), where \(\theta=\omega t\) and \(\omega=\) angular velocity of gears, will be developed, causing the table to vibrate. Design a vibration table that can develop a force in the range \(0-100 \mathrm{~N}\) over a frequency range \(25-50 \mathrm{~Hz}\).

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G W FIGURE 1.121 A vibration table. -Spring m G Object being tested