18.03 Lecture Notes - Phugoid, Buckling, Attractor
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[1] the bob of a pendulum is attached to a rod, so it can swing clear around the pivot. L length of pendulum m mass of bob g acceleration of gravity. We will assume that the motion is restricted to a plane. To describe it we need a dynamical variable. We could use a horizontal displacement, but it turns out to be easier to write down the equation controlling it if you use the angle of displacement from straight down. Write theta for that angle, measured to the right. |theta mg | /\ (this is supposed to be a right angle!) Write s for arc length along the circle, with s = 0 straight down. The force has the - mg sin(theta) component of the force of gravity (and notice the sign! ), and also a frictional force which depends upon s" = l theta" Make the simplest model for friction, - cs" = -cl theta".
