The instrument shown in figure, with a mass of 20 kg is attached to platform P that rests on four springs, each having a stiffness of 980 N/m. The floor is subjected to a vertical acceleration x(t) = 200 sin 8 t mm/s. 65 x(t) X(t) a) what is the frequency of the floor required to cause resonance? b) write the equation of motion of the platform c) determine the displacement of the floor xf(t) as a function of time d) determine the amplitude of the displacement of the platform relative to the floor. e) determine the maximum amplitude of the vibration of the instrument.