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exam01_sample_problems

# exam01_sample_problems - Fall 2007 PROBLEM 1(40 Consider...

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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

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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 0 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: 0 ) 0 ( y y ! ! = , 0 ) 0 ( y y = , and 0 ) 0 ( u u = . (b) Now, let 10 0 = y ! , 1 0 ! = y , and 1 0 = u . Find y(t) when u(t) is a unit impulse. (c) What is the transfer function from u to y for this system?
Spring 2002 - PROBLEM NO. 1 (50%) Modeling of a Mechanical System Consider the mechanical system illustrated in Fig. 1.1. The mass of the disk is M d and it is uniformly distributed. There is no friction between the cart and ground. There is also NO friction between the disk and the cart . We are interested in horizontal motion only and assume that the rotational angle of the disk is very small. The outputs that we are interested in are the spring force caused by spring K 2

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exam01_sample_problems - Fall 2007 PROBLEM 1(40 Consider...

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