SYSC 3600 – Assignment #111/. An electric motor has a mounting that can be approximated by the combination of a spring and a damper (see diagram below). Assume that the mass of the motor is 20kg, that the spring constant is 493.5 kN/m, and that the damping co-efficient is 6.28N/(m/s). If the motor is rotating at 1500 rpm and a rotating imbalance causes it to be subject to a sinusoidal force that varies between +25N and –25N, how much will the motor vibrate? 2/. Now suppose that we attach a device consisting of a mass, a spring, and a damper to the motor (as shown below). Assume that m2is 1kg, k2is 22.38kN/m, and that c2is 40N/(m/s). Model the system using state space techniques and obtain its transfer function using two different techniques (note: algebraic manipulation of the frequency domain versions of the state space equations works very well here). Under the same operating conditions, how much will the modified motor vibrate? If your results are correct, it should be apparent why the device is called a vibration absorber.
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