An electric motor of mass *D* kg is supported by springs of total effective stiffness 100 N/m and negligible damping. It is operating at 1600 rpm. a) Given that the motor has an unbalance equivalent to a mass of 10 g a distance of 50 mm from the axle, show that there is a driving force amplitude of oscillation of 14 N. b) Calculate the natural angular frequency of the motor in rad/s. [2 marks] c) By comparing the operating frequency of the motor to its natural frequency, what does this tell us about the amplitude of oscillations of the motor and the phase between the displacement of the motor and the driving force (without further calculation)? Max. 100 words. [2 marks] Suppose now that the motor is set to operate at a much lower rate of 400 rpm for the rest of this question. d) Calculate the resulting amplitude of oscillation of the motor. [4 marks] e) To avoid damage to surrounding components, the amplitude of oscillation must be kept to 4 mm. Calculate the minimum damping constant of a damper that should be added to the motor support to comply with this requirement. f) Calculate the phase angle by which the displacement lags the driving force? [3 marks] g) Calculate the magnitude of the force transmitted to the surrounding structure and the transmissibility. h) Calculate the phase angle between the transmitted force and the driving force. i) Calculate the phase angle between the driving force and the transmitted force. [4 marks] [3 marks] [3 marks] [2 marks]