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[25 marks] A motor is supported on a machine-bed in the manner illustrated in Figure Q1. The motor is out of balance, so that when it is rotating at its operating speed it subjects the machine-bed to a harmonic force in the vertical direction. This force is: F(t) = 50 sin(20t) N The motor and machine-bed are supported on a support that can be modelled as a mass-spring-dashpot system. The combined mass of the electric motor and the machine-bed is 30 kg. The coefficient of damping c is 75 Ns/m. The stiffness of the elastic support k is 900 N/m. a) Calculate the frequency of the forcing function in Hz. [2] b) Determine the equation for steady state vibration of the mass and the magnitude of the phase angle . [6] c) Calculate the magnitude of the undamped natural frequency w of the mass- spring system, in the absence of the dashpot (assume for this question only that the dashpot has been temporarily removed). [3] d) Calculate the magnitude of the damping ratio 3. [3] e) Calculate the damped frequency w of the mass-spring-dashpot system, in the presence of the dashpot. [3] f) If the machine remains out of balance, and the operating speed of the machine is increased slightly, what will be the effect on the forces acting on the support and the steady state motion of the support? Give a full answer which includes the forcing frequency and amplitude, the frequency and dynamic amplifier of the motion, and the phase angle. Your answer should refer to the resonance diagram found in the equation sheet. m = 30 kg k = 900 N/m Base Figure Q1 1 F(t)= = 50 sin (20t) N c = 75 Ns/m [8]