MASSACHUSETTS INSTITUTE OF TECHNOLOGYDepartment of Mechanical Engineering2.004 Dynamics and Control IIFall 2007Problem Set #4Posted: Friday, Sept. 28, ’07 Due:Friday, Oct. 5, ’071. (a) Problem 21(a) from Nise textbook, Chapter 2 (page 113). (b) After youfind the transfer function, locate the zeros and poles, draw them on the s–plane,and determine the type of the response of the system (undamped, underdamped,critically damped, or overdamped).2. Problem 25 from Nise textbook, Chapter 4 (page 236).3. Derive the transfer function of the electrical network shown below with the sourcevoltage vs(t) as input and the voltage vc(t) across the capacitor as output, whereR2= 10Ω, L = 1 mH, C =10μF andi) R1= 5Ω;ii) R1= 100Ω.CR1R2vs+-vc+-LFor each case,a) locate the zeros and poles and draw them on the s–plane;b) determine the type of the response (undamped, underdamped, criticallydamped, or overdamped);c) if you find that the system is underdamped, determine the natural frequency,the damped frequency, the settling time and the percent overshoot (%OS);if, on the other hand, you find that the system is overdamped, determine thetwo time constants;d) determine the steady–state value directly from the transfer function;e) plot the response to a step voltage of magnitude 5 V and verify that itmatches your answers to the previous questions.14. Consider again the system of a compliant mass driving a shaft that we modeled inPS01/4.a and derived the transfer function for in PS02/4. Substitute numericalvalues M = 1 kg, J =1kg· m2, fv=2kg/ sec, r =0.1 m, and two cases oftranslational compliancei) K =0.1N/ m;ii) K =1.0N/ m.For each case,a) find the poles of the system (you can use the roots function in Matlab ,or any numerical analysis software of your choice);b) determine if the system has dominant poles;c) sketch by hand the step response of the system as accurately as you canfrom the transfer function but without solving for the exact solution. Donot use any numerical analysis tools for this part of the
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