A motor mounted on a cantilever beam weighs 20 lb and runs at the constant speed of 3500 rpm. The steel beam is 6 in. long, 4 in. wide, and 3/8 in. thick. The unbalanced part of the motor weighs 1 lb and has an eccentricity of 0.01 ft. The damping in the beam is very slight. Design a vibration absorber for this system. The available clearance for the absorber's motion is 0.25 in. Use E = 3 ×107 psi for the modulus of elasticity of steel. Use ( = 15.2 slug/ft3 for the density of steel.