Vibration - Equation of motion Q A machine having a mass of 1500 kg is mounted on supports which provide an effective vertical stiffness of 4.5 MN/m. The machine is subjected to a vertical harmonic force having an amplitude of 200 N at a frequency equivalent to 80% of the natural frequency of the machine on its mounting. It is proposed to minimise all the vertical vibrations of the machine by fitting a vibration absorber. 1. Set up the equations of motion for the combined machine-absorber system and hence obtain an expression for the characteristic equation. 2. Determine the stiffness and mass of a suitable absorber if the amplitude of the absorber mass is to be limited to 10 mm at the forcing frequency.