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# Centre of Oscillation

## axis, body and suspension

CENTRE OF OSCILLATION (Lat. oseilla tio, a swinging). The period of oscillation of a simple pendulum—i.e. of a minute particle of matter vibrating through a small amplitude at the end of a fine thread which is supposed to be without weight, is given by the formula: T ='27r / where r = 3.141(t. / is the length of the thread, and q is the acceleration of a falling body due to gravity. Thus. the period varies as the square root of the length of the pendulum. If. however. the vibrating body is a large solid oscillating about a fixed axis, the period of oscillation is given by the formula ' \ where I is the moment of inertia around the axis of suspension, is the mass of the body, and h is the perpendicular distance from the axis of suspension to the centre of gravity of the body.

If each particle of the vibrating body were separately connected with the axis of suspen sion by a tine thread and entirely disconneeted from the rest of the body. it would form a simple pendulum; hut in general its period would not be that of the body itself. Those

nearest the axis of suspension would also vibrate in a shorter time than those farther away. As a rule it is possible. however, to find a series of particles vibrating as simple pendulums. would have the same period as that of the body. Their from the axis of suspension evi dently given by the condition = „- , or Jlh If a line can be drawn in the body parallel to the axis of suspension, at the distance I from it, and so that the plane of the two lines includes the centre of gravity, it is called the of oscillation.' with reference to the given axis of suspension. It may be shown that if the body be suspended so as to vibrate about the axis of oscillat" . the former axis of suspension will be the new axis of oscillation. and the period of vibration is the same in both cases. The inter section of the axis of oscillation by a plane pass ing through the centre of gravity and perpen dicular to the axis is called the 'centre of oscil lation.'