MVDJJJUD sinal Examination age 4 01 QUESTION 2 [25 MARKS] (a) A spring-mass system where a mass m is connected to a fixe

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Mvdjjjud Sinal Examination Age 4 01 Question 2 25 Marks A A Spring Mass System Where A Mass M Is Connected To A Fixe 1 (157.88 KiB) Viewed 35 times

MVDJJJUD sinal Examination age 4 01 QUESTION 2 [25 MARKS] (a) A spring-mass system where a mass m is connected to a fixed base via a spring of stiffness k and a damper with damping coefficient c is shown in Figure 1. The rollers are assumed to be frictionless. Draw the free body diagrams for the system, clearly indicating any assumptions used and the directions of forces and displacements. xi(t) x2(t) k F(t) m w O O Figure 1 (For Question 2a) (b) Using the 'inverting' configuration of OP-Amps, sketch a circuit to perform a sum of two voltage signals vi(t) and v2(t). (C) For a second order system with a pair of dominant complex conjugate poles with real parts of -2, sketch step responses for the three cases when an additional 'zero' is included at s = – 4, s=-10, and s = +4, paying attention to the differences and commenting on them. (d) The equation of motion for a DC motor that drives an equivalent inertia referred to the motor axis using applied voltage input v, is given by the following differential equation: 0.01 Öm + 0.03 m = 0.1 va, where the input voltage v, is given in Volts while the output motor shaft angle Om is given in radians, and all derivatives are expressed w.r.t. time. i) Find the transfer function between the applied voltage v, and the motor shaft angle om, and determine the system type. ii) Using the result from part (i) or otherwise, find the transfer function between the applied voltage v, and the motor speed ºm. iii) Using the transfer function obtained in part (i), draw a feedback diagram if this motor is to be used for position control employing a simple proportional controller. (e) Given the open loop transfer function (s + 10) G(S) = s(s+20)(8 + 30) write MATLAB scripts on your answer sheet for plotting a (i) unit step response (ii) root locus plot.