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midterm2_spring10

# midterm2_spring10 - Midterm 2 Solutions Spring 10 1 6.01...

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Midterm 2 Solutions — Spring 10 1 6.01 Midterm 2: Spring 2010 Name: Section: Solutions: Not correct for the make-up exam. Enter all answers in the boxes provided. During the exam you may: read any paper that you want to use a calculator You may not use a computer, phone or music player For staff use: 1. /16 2. /16 3. /8 4. /25 5. /5 6. /8 7. /12 8. /10 total: /100

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1 Midterm 2 Solutions — Spring 10 2 Pole Position (16 points) The polar plot shows the dominant pole for several systems. Match each pole to the unit sample response of the system. 1.5 1.0 0.5 0.5 1.0 1.5 1.5 1.0 0.5 0.5 1.0 1.5 1 8 7 6 5 4 3 2 10 20 30 40 - 500000 500000 1.0 · 10 6 1.5 · 10 6 2.0 · 10 6 10 20 30 40 20 40 60 80 10 20 30 40 0.5 1.0 1.5 2.0 A = 1 B = 6 C = 7 10 20 30 40 - 1.0 - 0.5 0.5 1.0 1.5 2.0 10 20 30 40 - 1.5 - 1.0 - 0.5 0.5 1.0 1.5 2.0 10 20 30 40 0.5 1.0 1.5 2.0 D = 8 E = 3 F = 5 10 20 30 40 - 1.5 - 1.0 - 0.5 0.5 1.0 1.5 2.0 10 20 30 40 - 0.5 0.5 1.0 1.5 2.0 G = 2 H = 4
2.2 2.3 2.4 Midterm 2 Solutions — Spring 10 3 2 What’s the difference? (16 points) Assuming the voltage at node N 0 = 0 , compute the voltage at node N 1 in each of these circuits. 2.1 R + _ + _ + _ R R R V V V N 1 N 0 V/2 R R R R I N 1 N 0 IR R R R R I I I N 1 N 0 3IR R + _ + _ + _ R R R V V V N 1 N 0 3V/4

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Midterm 2 Solutions — Spring 10 4 Scratch Paper
Midterm 2 Solutions — Spring 10 5 3 Op Amps (8 points) For each of the following circuits, give the output voltage V 0 as a function of the input voltage sources, input current sources, and resistances. Assume the op-amps are ideal. 3.1 V 1 - + + _ + _ V 3 V 0 + _ V 2 R R R R 3.2 - + R 1 R 2 I V 0 V 1 V 2 0

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4 Midterm 2 Solutions — Spring 10 6 Motor control (25 points) WhizzyLand engineers Kim, Pat, Jody, Chris, and Jamie are trying to design a controller for a display of three dancing robotic mice, using a 10V power supply and three motors. The first is supposed to spin as fast as possible (in one direction only), the second at half of the speed of the first, and the third at half of the speed of the second. Each engineer has come up with a design, as shown below. Assume the motors have a resistance of approximately 5Ω and that rotational speed is proportional to voltage. For each design, indi- cate the voltage across each of the motors. Your answer only needs to be within 0.5V of the correct answer.
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