When a rigid body is suspended vertically and it oscillates with a small amplitude under the action of force of gravity, the body is known as compound pendulum, as shown in Fig. 1.35.
For a compound pendulum, the periodic time is given by
![Periodic time for compound pendulum Periodic time for compound pendulum](data:image/png;base64,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)
and frequency of oscillation,
![frequency of oscillation for compound pendulum frequency of oscillation for compound pendulum](data:image/png;base64,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)
where
kG = Radius of gyration about an axis through the center of gravity G and perpendicular to the plane of motion, and
h = Distance of point of suspension from the center of gravity G.
Notes:
1. The equivalent length of a simple pendulum (L) which gives the same frequency as that of compound pendulum is given by
![Equivalent length of a simple pendulum Equivalent length of a simple pendulum](data:image/png;base64,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)
2. The periodic time of compound pendulum is minimum when the distance between the point of suspension and the center of gravity (i.e. h) is equal to the radius of gyration of the body about its center of gravity (i.e. kG).
So, Minimum periodic time of a compound pendulum,
and frequency of oscillation,
where
kG = Radius of gyration about an axis through the center of gravity G and perpendicular to the plane of motion, and
h = Distance of point of suspension from the center of gravity G.
Notes:
1. The equivalent length of a simple pendulum (L) which gives the same frequency as that of compound pendulum is given by
2. The periodic time of compound pendulum is minimum when the distance between the point of suspension and the center of gravity (i.e. h) is equal to the radius of gyration of the body about its center of gravity (i.e. kG).
So, Minimum periodic time of a compound pendulum,
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