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Assignment 3-Questions

Assignment 3-Questions - m ¨ x =-kx-b ˙ x u t where you...

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ECE3085 - Homework #3 Due: Jan. 28, 2009 Problem 1. (5 pts) Compute the inverse Laplace transform of F ( s ) = 1 s ( s + 2) 2 Problem 2. (5 pts) The DC gain of a system is the steady-state response of the system to a unit step input. In more mathematical terms, that would mean the limit of the time response as t goes to infinity. What is the the DC gain of the system Y ( s ) = G ( s ) U ( s ) = s + 7 ( s + 1)( s 2 + 4) U ( s ) Problem 3. (10 pts) Solve for the following differential equation using the Laplace transform ¨ y + y = t, y (0) = 1 , ˙ y (0) = - 1 . Problem 4. (10 pts) Solve for the following differential equation using the Laplace transform ¨ y - y + 4 y = t, y (0) = 3 , ˙ y (0) = - 1 . Problem 5. (15 pts) You are an engineer for Cadillac cars and want to design the suspension system for the back seats of the car. You have decided on the mass-spring-damper model for the system dynamics,
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Unformatted text preview: m ¨ x =-kx-b ˙ x + u ( t ) where you are assuming that the nominal mass of a person on board the car will be about 90 kg. When you call the parts department for possible parts, they tell you that the only options for you are two packages available. One package with a spring whose constant is k 1 = 12960 kg m and damper whose coefficient is b 1 = 1680 kg s/m. Another package comes with the spring constant/damping coefficent of k 2 = 2250 kg m and and b 2 = 300 kg s/m. Which package do you pick for your system to give a more pleasing ride? In this case, a more pleasing ride is determined by the time response to a unit step. In particular, you want for the peak response to be as low as possible....
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