Machinery's Handbook, 31st Edition
180
Pendulums Pendulums
A compound or physical pendulum consists of any rigid body suspended from a fixed horizontal axis about which the body may oscillate in a vertical plane due to the action of gravity. A simple or mathematical pendulum is similar to a compound pendulum except that the mass of the body is concentrated at a single point which is suspended from a fixed horizon tal axis by a weightless cord. Actually, a simple pendulum cannot be constructed since it is impossible to have either a weightless cord or a body whose mass is entirely concentrated at one point. A good approximation, however, consists of a small, heavy bob suspended by a light, fine wire. A pendulum that does not meet these conditions should be considered a compound pendulum. A conical pendulum is similar to a simple pendulum except that the weight suspended by the cord moves at a uniform speed around the circumference of a circle in a horizontal plane instead of oscillating back and forth in a vertical plane. The principle of the conical pendulum is employed in the Watt fly-ball governor. Four Types of Pendulum
O
O
r
G
W
W
Physical Pendulum
Simple Pendulum
O
d
W
r Torsional Pendulum
r
Conical Pendulum
W = Weight of Disk A torsional pendulum in its simplest form consists of a disk fixed to a slender rod, the other end of which is fastened to a fixed frame. When the disc is twisted through some angle and released, it will oscillate back and forth about the axis of the rod because of the torque exerted by the rod. Pendulum Formulas.— From the formulas that follow, the period of vibration or time required for one complete cycle back and forth may be determined for the types of pendu lums shown in the accompanying diagram.
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