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# NCERT Textbook - Oscillations Class 11 Notes | EduRev

## Class 11 : NCERT Textbook - Oscillations Class 11 Notes | EduRev

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CHAPTER FOURTEEN
OSCILLATIONS
14.1 INTRODUCTION
In our daily life we come across various kinds of motions.
motion and motion of a projectile. Both these motions are
non-repetitive. We have also learnt about uniform circular
motion and orbital motion of planets in the solar system. In
these cases, the motion is repeated after a certain interval of
time, that is, it is periodic. In your childhood you must have
enjoyed rocking in a cradle or swinging on a swing. Both
these motions are repetitive in nature but different from the
periodic motion of a planet. Here, the object moves to and fro
about a mean position. The pendulum of a wall clock executes
a similar motion. Examples of such periodic to and fro motion
abound : a boat tossing up and down in a river, the piston in
a steam engine going back and forth, etc. Such a motion is
termed as oscillatory motion. In this chapter we study this
motion.
The study of oscillatory motion is basic to physics; its
concepts are required for the understanding of many physical
phenomena. In musical instruments like the sitar, the guitar
or the violin, we come across vibrating strings that produce
pleasing sounds. The membranes in drums and diaphragms
in telephone and speaker systems vibrate to and fro about
their mean positions. The vibrations of air molecules make
the propagation of sound possible. In a solid, the atoms vibrate
about their equilibrium positions, the average energy of
vibrations being proportional to temperature. AC power
supply give voltage that oscillates alternately going positive
and negative about the mean value (zero).
The description of a periodic motion in general, and
oscillatory motion in particular, requires some fundamental
concepts like period, frequency, displacement, amplitude and
phase. These concepts are developed in the next section.
14.1 Introduction
14.2 Periodic and oscillatory
motions
14.3 Simple harmonic motion
14.4 Simple harmonic motion
and uniform circular
motion
14.5 Velocity and acceleration
in simple harmonic motion
14.6 Force law for simple
harmonic motion
14.7 Energy in simple harmonic
motion
14.8 Some systems executing
SHM
14.9 Damped simple harmonic
motion
14.10 Forced oscillations and
resonance
Summary
Points to ponder
Exercises
Appendix
not to be republished
Page 2

CHAPTER FOURTEEN
OSCILLATIONS
14.1 INTRODUCTION
In our daily life we come across various kinds of motions.
motion and motion of a projectile. Both these motions are
non-repetitive. We have also learnt about uniform circular
motion and orbital motion of planets in the solar system. In
these cases, the motion is repeated after a certain interval of
time, that is, it is periodic. In your childhood you must have
enjoyed rocking in a cradle or swinging on a swing. Both
these motions are repetitive in nature but different from the
periodic motion of a planet. Here, the object moves to and fro
about a mean position. The pendulum of a wall clock executes
a similar motion. Examples of such periodic to and fro motion
abound : a boat tossing up and down in a river, the piston in
a steam engine going back and forth, etc. Such a motion is
termed as oscillatory motion. In this chapter we study this
motion.
The study of oscillatory motion is basic to physics; its
concepts are required for the understanding of many physical
phenomena. In musical instruments like the sitar, the guitar
or the violin, we come across vibrating strings that produce
pleasing sounds. The membranes in drums and diaphragms
in telephone and speaker systems vibrate to and fro about
their mean positions. The vibrations of air molecules make
the propagation of sound possible. In a solid, the atoms vibrate
about their equilibrium positions, the average energy of
vibrations being proportional to temperature. AC power
supply give voltage that oscillates alternately going positive
and negative about the mean value (zero).
The description of a periodic motion in general, and
oscillatory motion in particular, requires some fundamental
concepts like period, frequency, displacement, amplitude and
phase. These concepts are developed in the next section.
14.1 Introduction
14.2 Periodic and oscillatory
motions
14.3 Simple harmonic motion
14.4 Simple harmonic motion
and uniform circular
motion
14.5 Velocity and acceleration
in simple harmonic motion
14.6 Force law for simple
harmonic motion
14.7 Energy in simple harmonic
motion
14.8 Some systems executing
SHM
14.9 Damped simple harmonic
motion
14.10 Forced oscillations and
resonance
Summary
Points to ponder
Exercises
Appendix
not to be republished
14.2 PERIODIC AND OSCILLATORY MOTIONS
Fig. 14.1 shows some periodic motions. Suppose
an insect climbs up a ramp and falls down it
comes back to the initial point and repeats the
process identically. If you draw a graph of its
height above the ground versus time, it would
look something like Fig. 14.1 (a). If a child climbs
up a step, comes down, and repeats the process,
its height above the ground would look like that
in Fig. 14.1 (b). When you play the game of
bouncing a ball off the ground, between your
palm and the ground, its height versus time
graph would look like the one in Fig. 14.1 (c).
Note that both the curved parts in Fig. 14.1 (c)
are sections of a parabola given by the Newton’s
equation of motion (see section 3.6),
2
1
2
+ gt h=ut
for downward motion, and
2
1
2
– gt h=ut
for upward motion,
with different values of u in each case. These
are examples of periodic motion. Thus, a motion
that repeats itself at regular intervals of time is
called periodic motion.
Fig. 14.1 Examples of periodic motion. The period T
is shown in each case.
Very often the body undergoing periodic
motion has an equilibrium position somewhere
inside its path. When the body is at this position
no net external force acts on it. Therefore, if it is
left there at rest, it remains there forever. If the
body is given a small displacement from the
position, a force comes into play which tries to
bring the body back to the equilibrium point,
giving rise to oscillations or vibrations. For
example, a ball placed in a bowl will be in
equilibrium at the bottom. If displaced a little
from the point, it will perform oscillations in the
bowl. Every oscillatory motion is periodic, but
every periodic motion need not be oscillatory.
Circular motion is a periodic motion, but it is
not oscillatory.
There is no significant difference between
oscillations and vibrations. It seems that when
the frequency is small, we call it oscillation (like
the oscillation of a branch of a tree), while when
the frequency is high, we call it vibration (like
the vibration of a string of a musical instrument).
Simple harmonic motion is the simplest form
of oscillatory motion. This motion arises when
the force on the oscillating body is directly
proportional to its displacement from the mean
position, which is also the equilibrium position.
Further, at any point in its oscillation, this force
is directed towards the mean position.
In practice, oscillating bodies eventually
come to rest at their equilibrium positions,
because of the damping due to friction and other
dissipative causes.  However, they can be forced
to remain oscillating by means of some external
periodic agency.  We discuss the phenomena of
damped and forced oscillations later in the
chapter.
Any material medium can be pictured as a
collection of a large number of coupled
oscillators. The collective oscillations of the
constituents of a medium manifest themselves
as waves.  Examples of waves include water
waves, seismic waves, electromagnetic waves.
We shall study the wave phenomenon in the next
chapter.
14.2.1 Period and frequency
We have seen that any motion that repeats itself
at regular intervals of time is called periodic
motion. The smallest interval of time after
which the motion is repeated is called its
period. Let us denote the period by the symbol
T. Its S.I. unit is second. For periodic motions,
OSCILLATIONS 337
(a)
(b)
(c)
not to be republished
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