A small electric motor of mass 40 kg is resting at the midspan of a simply supported beam of length 2 m, depth 36 cm and modulus of elasticity of 200 GPa. The ground on which the beam is supported oscillates vertically by y(t) = Y sin 100t. The equivalent damping ratio of the system is estimated to be 0.1. Calculate the necessary value of the thickness of the beam such that the amplitude of displacement of the motor measures 20% of the ground's amplitude. y(t) t -2 m z(t)