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Write equation of motion (Newton's Law) modeling a pendulum; find equilibrium points

A pendulum is modeled by a mass m, attached to one end of a light rod of lenght l, whose other end is attached to an axis. Write down the equation of motion (Newton's Law) modeling the pendulum. Rewrite the model as a system of two first order equations for the position and velocity of the mass. Find the equilibrium points and sketch them in the phase plane. Determine which equilibrium points are stable, which unstable.

Solution Preview

SEE ATTACHMENT #1 for a diagram showing parameters.

Let L = the length of a light (negligible mass) rod, attached to a fixed axis at one end, with mass m attached to the other.

Step 1.
Note the illustration of unstable position, (with the mass directly above the ...

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