One end of a uniform rigid bar of mass \(m\) is connected to a wall by a hinge joint \(O\), and the other end carries a concentrated mass \(M\), as shown in Fig. 2.127. The bar rotates about the hinge point \(O\) against a torsional spring and a torsional damper. It is proposed to use this

mechanism, in conjunction with a mechanical counter, to control entrance to an amusement park. Find the masses \(m\) and \(M\), the stiffness of the torsional spring \(\left(k_{t}\right)\), and the damping force \(\left(F_{d}\right)\) necessary to satisfy the following specifications: (1) A viscous damper or a Coulomb damper can be used. (2) The bar has to return to within \(5^{\circ}\) of closing in less than \(2 \mathrm{~s}\) when released from an initial position of \(\theta=75^{\circ}\).

Transcribed Image Text:

Fa Amusement park Bar (mass m) M k -1 = 45" FIGURE 2.127 Amusement park gate. Entrance