Question

The model in the figure is in equilibrium in the position shown: and a horizontal harmonic force is applied at the end of the bar (F = 0.5 sin(wet); in Newtons). Determine the ranges of wo, so that the amplitude of particular displacements of the bar is less than 25 mm. The uniform disks of radius 0.5 m and 2 Kg (each) are connected to the bar by means of joints located 0.5 m from the ends this. The discs roll without slipping. The bar AB is 3m long and weighs 9.81 N. The springs have a natural length of L. = V2 m and an elastic constant of K = 50 N/m. Consider x/L<< 1. 45 45° 45

Answer 1

The free body diagram of the system with the respective forces is shown. Two equations of motion are written, one for the translation motion of the bar and other for the rotational motion of the disc. The equation for translation motion of the bar will consist of the force terms while the equation for the rotational motion of disc will consist of torque term taken about point C. Both the obtained equation are solved for the maximum limit of x and then the range of values of ω are obtained.