# hw5 - Fall 2008 AME451 Homework#5 1 A thermometer requires...

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Fall 2008 AME451: Homework #5 1. A thermometer requires 1 min to indicate 98% of the response to a step input. a. Assuming the thermometer to be a first order system, find its time constant. b. If the thermometer is placed in a bath, the temperature of which is changing linearly at 10 deg/min, how much error does the thermometer show? 2. A closed-loop system transfer function has two dominant conjugate poles. Sketch the region in the left hand side of the complex plane (s-plane) where the complex poles should be located to meet the given specifications: a. 0 6 0 8 10 n . . , ≤ ζ ≤ ω ≤ b. 0 5 0 707 10 n . . , ≤ ζ ≤ ω ≥ c. 0 5 5 10 n . , ζ ≥ ≤ ω ≤ d. 0 707 5 10 n . , ζ ≤ ≤ ω ≤ e. 0 6 6 n . , ζ ≥ ω ≤ f. 0 5 0 707 6 d . . , ≤ ζ ≤ ω 3. Problem E5.8 in the textbook. 4. A closed-loop system transfer function has two dominant conjugate poles. Sketch the regions in the

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