Homework1_2010

# Homework1_2010 - ME580 Nonlinear Systems Home work#1 Due...

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ME580 Nonlinear Systems Home work #1 Due: Sept. 7, 2010 1. Consider the second-order linear system presented in class: 0 cos( ); mx cx kx F t  m , c , k 0. Non-dimensionalize the above system to 2 0 2 ( / )cos( ), nn x x x F m t  and find the complete solution for arbitrary initial conditions of 00 (0) , (0) x x x x  , assuming that 0 1. Now, specialize the solution in (a) to the undamped case of 0, and set 0 x to zero. This solution consists of two frequencies and we now want to explore the nature of this solution. i) Let 0.5, / 1.0, 4.0 n x F m and 0.5  . Plot the solution x ( t ) as a function of time; Plot the solution in the phase plane ( ( , ) xx plane); Now pick the initial condition x 0 such that no contribution comes from the free response, and again plot the solution x ( t ) as a function of time as well as in phase plane. Comment on all these solution plots. ii) Repeat the work in part (i) above with 0.5 n and 4.0 .

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Homework1_2010 - ME580 Nonlinear Systems Home work#1 Due...

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