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Task 1 In your Matlab script file, write the code required to find the eigenvalues ( lambda 1 and lambda 2 ) and
Task In your Matlab script file, write the code required to find the eigenvalues lambda and
lambda and the corresponding eigenvectors x and x for the matrix A Use the corresponding
section of the skeleton Matlab script at the end of this assignment. Run your script file to
find lambda lambda x and x Write your answers in your report.
The general solution of the system of equations will be a linear combination of all of the
solutions described above.
Question Write the general solution in terms of the eigenvalues and eigenvectors of the
matrix A
Hint: The system of equations consists of two second order linear ODEs. This means
that we should expect the general solution to have four arbitrary constants, that is the general
solution should be a linear combination of four solutions. Use c c c c for the arbitrary
constants.
The values of c c c c will depend on the initial conditions of the system, that is the specific
initial value problem. We will consider the following specific initial value problem:
z m z m
z m s
z m s
Question Give a physical interpretation of the initial conditions listed above in
Question To determine the unknown constants for any initial value problem, we can solve
a matrix equation of the form Bc d where c c c c c
T
Write down B and d
Task Then, in your Matlab script file, write the code required to find c c c c for the
specific initial value problem described above. Be sure, though, to set it up so that you can easily
change the initial value problem.
Our solution, Z describes the positions of the point masses at a particular time t
Task Fill in the necessary Matlab code required to calculate the positions of the masses at
times t seconds use a stepsize of s
To create the animation, we use the for loop within the skeleton Matlab code provided. Copy
this to your Matlab script file. Run the animation this will create Matlab Figure
Question Explain precisely what the lines of code marked with do
Task Create a Matlab figure that shows the path traced out by each mass as a function of
time ie for each mass, plot the position on the yaxis and time on the xaxis Show both traces
on the same figure. Only plot the graph for t using the axis command. Include a
printout of this figure in your report Figure
Question Explain why this does not need to be done inside the animation loop.
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