Two solid spheres of radius 3 in., weighing 2 lb each, are mounted at a and b on the horizontal rod a’b’, which rotates freely about the vertical with a counterclockwise angular velocity of 6 rad/s.

the spheres are held in position by a cord which is suddenly cut. knowing that the centroidal moment of inertia of the rod and pivot is iy = 0.25 lb-ft-s2, determine (a) the velocity of the spheres after they have moved to positions a’ and b’, (b) the energy lost due to the plastic impact of the spheres and the stops at a’ and b’.

calculate (a) by treating the spheres as points with the same mass while neglecting the mass of the rod and pivot.

Tom is having a problem with his washing machine. he notices that the machine vibrates violently at a frequency of 1500 rpm due to an unknown rotating unbalance. the machine is mounted on 4 springs each having a stiffness of 10 kn/m. tom wishes to add an undamped vibration absorber attached by a spring under the machine the machine working frequency ranges between 800 rpm to 2000 rpm and its total mass while loaded is assumed to be 80 kg a) what should be the mass of the absorber added to the machine so that the natural frequency falls outside the working range? b) after a first trial of an absorber using a mass of 35 kg, the amplitude of the oscillation was found to be 10 cm. what is the value of the rotating unbalance? c) using me-3.5 kg.m, find the optimal absorber (by minimizing its mass). what would be the amplitude of the oscillation of the absorber?