Find the natural frequencies and the natural modes of the overhead crane of Fig. 1.19 for “small-amplitude” oscillations about a stable equilibrium state, in the absence of damping. As well, assume that the slider travels at a uniform speed to the right, with the rod in a vertical, stable position, and subject to no external force. Under these conditions, the slider encounters a stationary obstacle on its way, with which it undergoes a perfectly elastic collision. Find the time response of the system if the speed of the slider just prior to the collision is v₀.

Find the natural frequencies and the natural modes of the overhead crane of Fig. 1.19 for “small-amplitude” oscillations about a stable equilibrium state, in the absence of damping. As well, assume that the slider travels at a uniform speed to the right, with the rod in a vertical, stable position, and subject to no external force. Under these conditions, the slider encounters a stationary obstacle on its way, with which it undergoes a perfectly elastic collision. Find the time response of the system if the speed of the slider just prior to the collision is v₀.

Transcribed Image Text:

g u(t) (given) m, l 0 M Fig. 1.19 Overhead crane driven by a motion-controlled source Vo (u) Vc/o (18/2)