The motion of the bob from one extremity to the other is known as beat or swing. Thus one beat = 1/2 oscillation.

At mean the value of x = 0. Therefore, it is maximum at mean position.

When a rigid body is suspended vertically, and it oscillates with a small amplitude under the action of the force of gravity, the body is known as compound pendulum. Thus the periodic time of a compound pendulum is minimum when the distance between the point of suspension and the centre of gravity is equal to the radius of gyration of the body about its centre of gravity.

We know that the periodic time,

Acceleration, aN = ω2.rcosθ = ω2.r.

Velocity of any particle vN = vsinθ = ω.rsinθ = ω √r2 − x2.

The centre of oscillation is sometimes termed as centre of percussion. It is defined as that point at which a blow may be struck on a suspended body so that the reaction at the support is zero. The centre of percussion is below the centre of gravity and at a distance k2G/h. The distance between the centre of suspension and the centre of percussion is equal to the equivalent length of a simple pendulum.

By comparing the frequencies of simple pendulum to compound pendulum we get the equivalent length of simple pendulum as k2G +h2/h.

Periodic time is the time taken for one complete revolution of the particle.

None.