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Where You Taught ”compound Pendulum” In Your Secondary School? - Education - Nairaland

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Where You Taught ”compound Pendulum” In Your Secondary School? by basketbrain(m): 9:02pm On Oct 30, 2014
I guess we re all used to simple pendulum; secondary physics. Remember those days, WAEC practicals the pendulum bob, string, calculating the number of oscillation and time taken. Good, but were you taught Compound pendulum? My answer No. Let me know if it was just my physics teacher being lazy.
Re: Where You Taught ”compound Pendulum” In Your Secondary School? by basketbrain(m): 9:32pm On Oct 30, 2014
Compound pendulum
The length L of the ideal simple pendulum discussed above
is the distance from the pivot point to the center of mass of
the bob. Any swinging rigid body free to rotate about a fixed
horizontal axis is called a compound pendulum or physical
pendulum. The appropriate equivalent length L for
calculating the period of any such pendulum is the distance
from the pivot to the center of oscillation.[16] This point is
located under the center of mass at a distance from the
pivot traditionally called the radius of oscillation, which
depends on the mass distribution of the pendulum. If most
of the mass is concentrated in a relatively small bob
compared to the pendulum length, the center of oscillation
is close to the center of mass.[17]
The radius of oscillation or equivalent length L of any
physical pendulum can be shown to be
where I is the moment of inertia of the pendulum about the
pivot point, m is the mass of the pendulum, and R is the
distance between the pivot point and the center of mass.
Substituting this expression in (1) above, the period T of a
compound pendulum is given by
for sufficiently small oscillations.[18]
A rigid uniform rod of length L pivoted about either end has
moment of inertia I = (1/3)mL2. The center of mass is
located at the center of the rod, so R = L/2. Substituting these
values into the above equation gives T = 2π√ 2L/3g . This
shows that a rigid rod pendulum has the same period as a
simple pendulum of 2/3 its length.
Christiaan Huygens proved in 1673 that the pivot point and
the center of oscillation are interchangeable.[19] This means
if any pendulum is turned upside down and swung from a
pivot located at its previous center of oscillation, it will have
the same period as before and the new center of oscillation
will be at the old pivot point. In 1817 Henry Kater used this
idea to produce a type of reversible pendulum, now known
as a Kater pendulum, for improved measurements of the
acceleration due to gravity.

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