hw6 - MEEN 364 Fall 2004 Homework Set 6 Due October 14,...

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MEEN 364 Homework Set 6 Fall 2004 October 7, 2004 Homework Set 6 – Due October 14, 2004 @ 5:00 PM 1. Consider the system shown in following figure. The differential equation of motion for the system is given below: R θ l + R l 0 sin ) ( 2 = + + + & & & R g R l l = length of the cord in the vertical position, R = radius of the cylinder (a) Find the equilibrium point of the system. (b) Linearize the differential equation about the equilibrium point found in part (a) using Taylor series expansion. (c) Simulate the response of the system for the linear and the non-linear case using the initial conditions 6 / π = , . Use l = 1 m, R = 0.2m. 0 = = & & & 2. A system is modeled by the following differential equation of motion: () 22 0.5 3 0 xx x x x −− + + = && & & (a) Find the equilibrium point(s) of the system. (b) Linearize the differential equation about the equilibrium point(s) found in part (a) using Taylor series expansion. 3. The governing differential equations of motion for the hanging crane shown in the figure below are given as follows: 1
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MEEN 364 Homework Set 6 Fall 2004 October 7, 2004 () ), ( ) ( sin )] ( [ ) ( cos ) ( ) ( ) ( , 0 ) ( cos ) ( ) (
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hw6 - MEEN 364 Fall 2004 Homework Set 6 Due October 14,...

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