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ME429 Fall 2009 HW1 Solution

# ME429 Fall 2009 HW1 Solution - Assigned on 05.10.2009...

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Assigned on 05.10.2009 Monday Due date 12.10.2009 Monday, beginning of the lecture ME429 Fall 2009 HW1 - SOLUTION 1) According to given damping ratios, damping coeefficients can be calculated as follows, 1 1 2 44.72 Ns/m c mk ζ = = 2 2 2 89.44 Ns/m c mk ζ = = respectively. One can easily state that the first system is critically damped and the other is overdamped, examining the damping ratios. Then, the equations of motion of a critically damped and an overdamped system can readily be written as follows, ( ) 1 1 rt x t Ate = 2 1 1 1 4 , 2 o c c mk r A v m - - - = = ( ) -11.18 1 5 m t x t te = , result of part a). ( ) ( ) 1 2 2 2 rt rt x t A e e = - 2 2 2 1,2 2 1 2 4 , 2 o c c mk v r A m r r - - = = - ( ) ( ) -41.72 -2.99 2 -0.129 m t t x t e e = - , result of part b). respectively. Note that the initial conditions are taken as 0 o x = and o o x v = dotnosp . Plots of the responses and the relevant MATLAB source code is provided below. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 time [s] x(t) [m] critically damped overdamped

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Assigned on 05.10.2009 Monday Due date 12.10.2009 Monday, beginning of the lecture 2)
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ME429 Fall 2009 HW1 Solution - Assigned on 05.10.2009...

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