Find all the equilibrium points and classify them

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Reference no: EM133364200

Question: Consider the system x - 2' -x

1. Find all the equilibrium points and classify them.

2. Find a conserved quantity.

3. Draw the contours of the conserved function. (You can use contourf function in Matlab or the equivalent in Python for this.) Draw the phase portrait of the system (using pplane or such). What do you observe and justify your observation.

4. Suppose we add a smallamount of damping. The new systemis x = y, y =?by + x - x, where 0 < b < 1. Is the system still conservative? Draw the phase portrait and comment on the changes you observe.

Reference no: EM133364200

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