10.4.  The Pendulum

A simple pendulum consists of a particle of mass m, attached to a frictionless pivot by a thin support wire of length L, as shown in the figure.

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If the mass is pulled aside by a small angle, q and released, the pendulum will swing back and forth in simple harmonic motion. It can be shown that the frequency of this motion is given by equation (10.16)

Note that the frequency does NOT depend on the mass of the particle suspended from the wire! Only the length of the wire and the value for the gravitational acceleration, g, affect the pendulum's motion.

Example 4  

A pendulum of length 4.0 m is pulled aside and released. Find (a) the frequency and period of the pendulum on earth, and (b) the frequency and period for the same pendulum on the moon (g' = 1.57 m/s2).

(a) Using equation (10.16),
The period is,
T = 1/f = 1/(0.25 Hz) = 4.0 s.
(b)If we take this pendulum to the moon,
T' = 1/f' = 1/(0.10 Hz) = 10 s.


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