2 solving for the second derivative of x we

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Unformatted text preview: re(1); plot(thist,yhist(:,1)); %plot xlabel('time (s)'); %xlabel ylabel('position (meters)'); %ylabel title('Time History of Position') %title legend('m'); %legend eigs(A) %eigenvalues of the A matrix Matlab Plots: Graph of mb Graph of ma Graph of m Graph of m over a timespan of 10,000 seconds matrix A’s eigenvalues: - 0.2408 - 55.7132i - 0.2408 +55.7132i - 4.7588 - 37.9570i - 4.7588 +37.9570i - 0.0004 - 9.9947i - 0.0004 + 9.9947i As you can see the mass does eventually die down to zero oscillation. However it takes nearly 10,000 seconds. The reason for this is that if we look at the real parts of the eigenvalues of the A matrix we see that two of them are very small (.0004). One over this value is the time constant for the mass m. So 1/.0004=2500 seconds. It takes 4- 10 of these time constants for the system to settle down to steady state....
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This document was uploaded on 02/17/2014.

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