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Unformatted text preview: Assignment 6, Mechtron/Sfwr Eng 4aa4 Sample Solution Question 1 [1 + 1 + 1 ] 1. Find the polar form of the complex number 3 + j 4 M = 3 2 + 4 2 = 5 = arctan(4 / 3) = 180 53 . 1 3 + j 4 = 5 126 . 9 2. Convert 120 60 to rectangular form 120 60 = 120 cos 60 + j 120 sin 60 120(0 . 5) + j 120(0 . 866) 60 + j 103 . 92 3. Convert 60 + j 103 . 93 to exponential form 60 + j 103 . 93 = 120 120 = 120 e j 2 / 3 continued on page 2 Page 2 of 9 Question 2 [2 + 2 ] A potentiometer is a simple electromechanical transducer that converts rotary motion of its shaft by an operator into a change in resistance. Assume the potentiometer shown in figure below can be rotated through a full 360 degrees angle to get an output e o of zero to 20 volts as a function of the angle of rotation . Find the gain of the potentiometer in V/deg and in V/rad . Figure 1: Potentiometer S4. A rotation of degrees corresponds to a fraction 360 in degrees or 2 in radians. e o = 360 20 V Or the gain e o = 20 360 = 1 18 V/deg Similarly in terms of radians e o = 20 2 = 3 . 18 V/rad Question 3 [2+ 2 + 6] Figures 2 shows the response of three first order systems having transfer function K s + a , where the values of K and a are different for the three systems. Answer the following questions with the help of this figure: 1. Which of the three graphs (1, 2, 3) represents a sytem with the highest time constant?...
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 Fall '11
 Bokhari

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