INTRODUCTION

A pendulum is a weight suspended from a fixed point,

free to swing back and forth. It consists of a point
mass (bob) suspended by a light, inextensible string
from a fixed support. The motion of a simple
pendulum is a classic example of oscillatory motion,
specifically simple harmonic motion (SHM), where the
pendulum swings periodically about its equilibrium
position.

1. DEFINITION:
 A simple pendulum is a mechanical system
where a point mass (the bob) is attached to a
string or rod of fixed length (L) and allowed to
swing freely under the influence of gravity.

2. OSCILLATORY MOTION:
 The pendulum's back-and-forth movement is
called oscillation. One complete oscillation is
when the pendulum moves from its starting
point, reaches the farthest point on the other
side, and returns to the starting point.

3. TIME PERIOD:
 The time it takes for one complete oscillation
is called the time period (T) of the pendulum.

4. SIMPLE HARMONIC MOTION (SHM):

 The motion of a simple pendulum is
approximately SHM for small angles of swing
(usually less than 15 degrees).

5. AMPLITUDE:
 The maximum displacement of the pendulum
bob from its equilibrium position is called the
amplitude.

6. USES:
 Pendulums have various applications,
including timekeeping (pendulum clocks),
seismometers for measuring earthquakes, and
even in some scientific instruments.

7. FREQUENCY:
 The frequency of the simple pendulum is
defined as the number of oscillations performed
per unit time.

 PARTS OF A PENDULUM
1. BOB:
 This is the mass that swings back and forth.
It can be a small sphere, a block, or any object
with a defined mass.

2. STRING OR ROD:
 This connects the bob to the pivot point. It
can be a lightweight string or a rigid rod.

3. FIXED POINT:
 This is the point from which the pendulum
hangs and where the string or rod is attached.

 FACTORS AFFECTING TIME PERIOD

1. LENGTH OF THE STRING (L):

 The time period is directly proportional to the
square root of the length of the string. This
means a longer string results in a longer time
period. The formula for the time period (T) is: T =
2π√(L/g), where 'g' is the acceleration due to
gravity.

2. ACCELERATION DUE TO GRAVITY (G):

 The time period is inversely proportional to
the square root of the acceleration due to gravity.
This means a higher 'g' (like on Jupiter) would
result in a shorter time period.

3. MASS OF THE BOB:

 The mass of the bob does not affect the time
period (for small oscillations).

 CONSERVATION OF ENERGY: As the pendulum

swings, its potential energy is converted to kinetic
energy and vice versa, but the total mechanical
energy remains constant (in an ideal, frictionless
system).

 RELATION OF PENDULUM WITH NEWTON’S FIRST

LAW OF MOTION: The Pendulum Theory is based
on Newton's First Law of Motion, which states
that a body at rest tends to stay at rest, and a
body in motion tends to stay in motion with the
same speed, and in the same direction, unless
acted upon by an unbalanced force.

 The position of the bob of the freely suspended

pendulum at rest is called its mean position, O.
 When the bob P is
released after
moving its free end
P slightly to one
side (say to point
A), it crosses the
point O, goes to
the other side (say
to point B), and
returns
constituting a to and fro motion about the point
O. This to and fro motion of a pendulum bob
along the same path passing through the mean
position is called oscillatory motion. A complete
to-and-fro motion constitutes one oscillation. The
time taken by the pendulum to complete one
oscillation is called its time period. In contrast,
the number of oscillations the pendulum makes in
one second is called its frequency of oscillation.
The unit for frequency in the SI system is the hertz
(Hz).

 The position of the bob at a maximum distance

from the mean position is called the extreme
position. There are two extreme positions (points
A and B) on either side of the mean position. The
 maximum departure of the pendulum from its
mean position (or half the length of the swing) is
called its amplitude.

 The distance between the point of suspension S

and the centre G of the spherical bob is defined as
the effective length of the pendulum, L, as shown
in figure.
L=l+h+r
 Where,
 l - the length of the thread,
 h - length of the hook (if any)
 r - radius of the pendulum bob
 As the
motion of
the
pendulum
repeats
itself, it is an
example of
periodic
motion. A
swing in the
park also has
a similar
motion.
 The force responsible for maintaining the
oscillations in the simple pendulum is called the
restoring force. Practically, the amplitude of
oscillation decreases over time. Thus, the
pendulum will not continue oscillating for a long
time. This occurs because the pendulum loses
energy in overcoming friction and air resistance.

 PENDULUM CLOCK
 An interesting application of the pendulum is the
pendulum clock, which was widely used to keep
track of time until the early 1900s. You may have
seen an antique grandfather clock with a
pendulum swinging back and forth at precise
time intervals. Notably, even when the amplitude
of the simple pendulum changes, it takes the
same amount of time to complete one oscillation.
In many cases, these clocks had their pendulum
bob enclosed in glass cases to reduce the effects
of air resistance. Nowadays, pendulum clocks
have largely been replaced by quartz clocks, and
 you might have noticed the term "quartz" on
your wristwatches.

 LAWS OF SIMPLE PENDULUM

1. The time period of oscillation of a simple
pendulum with a constant length is independent
of its amplitude, provided that the amplitude is
sufficiently small.

2. The period of oscillation of a simple pendulum of

constant length is unaffected by the size, shape,
mass, or material of the bob, if the bob is not
very light.

3. The time period of oscillation of a simple

pendulum is directly proportional to the square
root of its length.
 BIBLIOGRAPHY
I. https://amrita.olabs.edu.in/?
sub=1&brch=1&sim=303&cnt=1
II. https://chatgpt.com/
III. https://www.youtube.com/
IV. https://byjus.com/
V. https://www.scribd.com/home