Homework 1, due January 23, 2008.

[goodwine]

1. Determine the equations of motion for the following two-mass system. Write them as a system of four first order ordinary differential equation.
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2. Determine the equations of motion for the following n-mass system. Write the second order differential equation for masses 1, 2, i and n. Also write them as a system of 2n first order ordinary differential equations.
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3. Determine the equations of motion for the three masses in the following figure. You do not have to convert these to a system of first order equations.
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4. Consider the matrix
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   1. Compute the eigenvectors and eigenvalues of this matrix by hand. Check your answer using Matlab.
   2. Pick a vector that is not one of the eigenvectors of A. Plot it and plot A times that vector. Observe that they are not colinear. Plot one of the eigenvectors and then plot A times that eigenvector. Obvserve that they are colinear and that the eigenvector has been scaled by the corresponding eigenvalue.
   3. Compute the product
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      where
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      Check this answer using Matlab.
   4. Using elementary row operations, solve the following equation for x
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      Again, check your answer using Matlab.
   Print and submit your work in Matlab along with your calculations done by hand.
5. Determine the general solution to to the scalar differential equation
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[tfurlong]

For question four, do we need to print out the checks we do on Matlab to turn in

[goodwine]

For question four, do we need to print out the checks we do on Matlab to turn in

You don't have to print them, but say what matlab gives you since it probably isn't exactly the same, but rather scaled from what you computed. The fact that eigenvectors aren't unique is part of the point of checking.