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3.1 Introduction

remarkable Italian scientist can very well be coined the “father of
technology”. In fact, from Chapter 2 of Galilei and Seeger (1966) [1],
one envisages Rome during that time to have been the centre of science
in Europe, and that Galileo’s fascination with oscillations around 1590
would only marvel the world over. For instance, his experiments and
observations with “measuring time”, as based on the notion of
mechanical “swings” and “vibrations”, would naturally enter our world
as the everyday time-keeping devices that today’s modern society refer
to as clocks and watches.
Around this time can be traced the earliest records of Galileo’s
concept of a simple pendulum, in which the motion of a suspended bob is
seen to undergo natural oscillations, is attributed to Galileo’s legendary
observations of a swinging chandelier in the Cathedral of Pisa (Chapter
15 of Galilei and Seeger (1966) [1]). It was these observations that led to
Galileo’s famous pendulum law, which Galileo himself formulated as the
law of isochronism, meaning equality of time – because a pendulum will
“sweep” back and forth at the same rate irrespective of the size or
amplitude of its swing.
In its most primitive form, Galileo used pendulum bobs made
of wooden objects or corks, as well as lead balls (e.g., see pp.17, Fermi
and Bernardini (1961) [2]), for his simple pendulum experiments.
Despite this simplicity, Galileo’s simple pendulum can still be simulated
perfectly, as shown in Figure 1, by using a light string (or weightless rod)
of constant length OA , which is suspended from one end at O and
having a “bob” of mass m attached to the other end, but at the same
time, is assumed to be freely “falling” under the influence of gravity g
in a vertical plane.
Initially, at time t seconds, the bob in Figure 1 is assumed to be
moving with speed , with its angle between the string and the
downward vertical OA at an angle radians. To frame this precisely, at
t t seconds, (t ) and (t ) radians. The conservation of
0 0 0 0 0
energy equation for the simple pendulum is, then, given by the relation

1 m 2 cos 1 2 cos ,
2 0 0 2
or
1 2 2 cos cos . (1)
2 0 0
Resolving tangentially along the arcAP s (see Figure 1)

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