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38 PENDULUM- VIBRATION [I. § 19.
c, d, respectively. If the pendulum is placed in the position Oa, and left to itself, it will reach an equally
inclined position on the other side of OA, i.e. will swing through twice the angle aOA before it turns back again. Similarly, if started at Ob it will swing through twice the angle bOA ; if at Oc, through twice the angle cOA ; and so on. Now the extremity of the pendulum, when at a, is further from the horizontal line, AD than when it is at b, since aa is greater than bb'; and when at b further than when at c. If we make the pendulum vibrate through only a small angle, by starting it, say, in the position Od, its extremity will throughout its motion be very near to the horizontal straight line AD. If we make the angle small enough, or, which is the same thing, take Ad sufficiently small compared with OA,