(^546) „„„„„ A Textbook of Engineering Mechanics
Fig. 26.12. Centre of
oscillation.
We know that extension of the spring,
δ = 0·3 sin θ = 0·3 × θ m
...(Q θ is very small, therefore substituting sin θ = θ)
and restoring force = s δ = 1800 × 0·3 θ = 540 θ N
Therefore restoring moment about A
= 540 θ × 0·3 = 162 θ N-m ...(i)
and disturbing moment about A = IA α = 1·02 α N-m ...(ii)
Equating equations (i) and (ii)
1·02 α = 162 θ
∴
162
158·8
1·0 2
α

θ
We know that frequency of oscillation,
11
158·8 2·01 Hz
22
n
α
== =
πθ π
Ans.
26.9. CENTRE OF OSCILLATION (OR CENTRE OF PERCUSSION)
It has been experimentally found that whenever a suspended body is given a blow, it causes:

1. the body to oscillate about the point of suspension O.


2. an impulse on the body.
   However, it has been experimentally found that there is always a point in the body, such that if
   a blow is given at that point, it will not produce any impulse on the body. Such a point is called centre
   of oscillation or centre of percussion e.g. in cricket, the batsman
   always intends to hit the ball at the centre of oscillation. But, if the
   ball is hit at some point, other than the centre of oscillation, the bat
   transmits a blow to the hands.
   The centre of oscillation (C) may also be defined as a point on
   the line joining the axis of suspension O and the centre of gravity (G)
   through which the resultant of the effective forces act as shown in
   Fig. 26.12.
   Consider a force (i.e. blow) P given to the body at C i.e.,
   centre of oscillation. Now consider two equal and opposite forces
   equal to P to be acting at G as shown in Fig. 26.12. A little
   consideration will show, that the forces will have the following
   effects on the body :


3. A force (P) acting at G which will produce a linear motion with an acceleration a.


4. A couple (with moment equal to P × l) which will tend to produce a motion of rotation in
   clockwise direction about the point G.