Bill Goodwine's Courses

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