ample_problems

ample_problems - Fall 2007 - PROBLEM 1 : (40%) Consider the...

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Unformatted text preview: Fall 2007 - PROBLEM 1 : (40%) Consider the following system. The mass slides without friction, and does not tip. Assume that the wheel rolls without slipping. The overall goal of this problem is to find the equations of motion (in proper form), using the parameter values and coordinate systems x and ! , where " is the input torque. a) Draw free body diagrams for all the elements in this system. Make sure to include all rotational & translational displacements and label all the forces and torques. b) \Write down the element law equations. c) Using ! ( t ) as the input to the system, provide the equations of motions in proper form. Box these equations so that it is clear what you have specified. x (t) m 1 K B ! (t), " (t) r I, m 2 R 2 Fall 2007 - PROBLEM 2: (30%) Consider the following equations of motion. u u x x y y y y y x x x 2 3 2 2 3 2 + = ! ! + + = ! ! + + ! ! ! ! ! ! ! ! ! (a) Determine the transfer function from u to x. (b) What is the corresponding input-output differential equation? Fall 2007 - PROBLEM 3: (30%) Consider the input/output equation: u u y y y + = + + ! ! ! ! 2 12 7 (a) find Y(s) where the initial condition are: ) ( y y ! ! = , ) ( y y = , and ) ( u u = . (b) Now, let 10 = y ! , 1 ! = y , and 1 = u . Find y(t) when u(t) is a unit impulse. (c) What is the transfer function from u to y for this system? October 7 th , 2010 Name 4 PROBLEM 2: (30%) A mass-spring-damper system has the following model m !! y + c ! y + ky = f ( t ) When a unit step input f ( t ) is applied to the system, the response y ( t ) has a 10% overshoot, a 2% settling time of 4 seconds, and a static gain of 2....
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ample_problems - Fall 2007 - PROBLEM 1 : (40%) Consider the...

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