At a client's site, there has been a vibration problem with an electric motor. The mass of the motor is 3.5 kg and sits on the tip of a cantilever beam which has an effective vertical stiffness of 250 kN/m at its tip as shown in the figure below. A viscous damper of coefficient 280 Ns/m is fitted at the underside off the beam directly below the motor and the other end grounded as shown in the figure. In order to assess the problem, the motor is depressed by 5mm and then released, its initial velocity is measured at 2.5m/s. Neglecting the mass of the beam. a) Calculate the natural frequency of the motor giving your answer in Hz and in rpm b) Determine the transient response of the system c) Plot the displacement response of the motor against time for the first 5 oscillations d) Use your knowledge of natural frequency to explain if it is suitable to operate the motor between 2500 rpm and 3000 rpm. (Guided word count: 150 words)