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114. Problem 15.49 (RHK) A pendulum is formed by pivoting a long thin rod of length
L and mass m about a point on the rod which is a distance d above the centre of
the rod. We have to find (a) the small-amplitude period of this pendulum
in terms of d, L, m, and g. (b) We have to show that the period has a
minimum value when
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Solution: Click For PDF Version It is given that a pendulum has been formed by pivoting a long thin rod of
length L and mass m about a point distance d from the
centre of the rod. The rotational inertia of the rod about its centre is
The small-amplitude period of SHM of this rod will be
Equivalently, we have
We will find the minimum value of T, by obtaining the equation of extremum
Its solutions is
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Using the parallel axis theorem the rotational inertia of the rod about an axis
passing through the pivot is found to be
