OSCILLATIONS
Chapter-14 OSCILLATIONS
Periodic motion: A motion that repeats itself at regular intervals of time is called periodic motion.
Ex: Motion of planets in solar system, uniform circular motion.
Oscillatory motion: A motion in which a body moves to and fro between two extreme positions
about an equilibrium position.
Ex: boat tossing up and down, piston of a steam engine, motion of simple pendulum.
Equilibrium (Mean) position: It is the position of a body during oscillatory motion at which the
net external force acting on the body is zero.
It is the position, at which if it is at rest, it remains at rest forever.
Oscillations or vibrations: The motion of a body between two extreme positions forms oscillations
or vibrations.
Note: (i) There is no significant difference between oscillations and vibrations. When the frequency
is small we call it oscillation, while the frequency is high we call it vibrations.
(ii) Every oscillatory motion is periodic; but every periodic motion need not be oscillatory.
Importance of oscillatory motion: This motion is basic to physics. In musical instruments we come
across vibrating strings, membranes in drums and diaphragms in telephone and speaker system
vibrate, vibrations of air molecule, vibrations of atoms in solid include oscillatory motion. The
concepts of oscillatory motion are required to understand many physical phenomena listed above.
Description of oscillatory motion: The description of oscillatory motion requires some
fundamental concepts like period, frequency, displacement, amplitude and phase.
Period or Time period (T): The smallest interval of time after which a periodic motion repeats is
called period.
In case of oscillation, the time taken by the body to complete one oscillation is called period. SI unit
of period is .
Frequency ( ): Number of times a periodic motion repeats per unit time is called frequency.
In case of oscillations, number of oscillations per unit time is called frequency. SI unit of frequency
is . oscillation per second.
Note: Relation between period and frequency is given by, ⁄ or ⁄
Displacement (x or y): The term displacement refers to change of physical quantity with time. In
periodic motion displacement may be linear as well as angular.
Linear displacement: The straight line distance travelled by a particle
from its equilibrium position.
Angular displacement: It is the angle through which position vector of the body rotates in a given
time.
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, OSCILLATIONS
Amplitude (A): The maximum displacement of the particle from its equilibrium
position is called amplitude.
Periodic function: Any function which repeats itself after a regular interval of time
is called periodic function.
In periodic motion displacement is periodic function and it can be represented by a mathematical
function of time. The simplest of these functions is given by, .
If is increased by an integral multiple of radian, the value of the function remains same and
is periodic.
( )
Note: (i) In , the term is called angular frequency.
(ii) The function is also periodic.
(iii) The linear combination of both sine and cosine function is also periodic and it is represented
by and it is called Fourier series.
By putting, and
√ ( )
Simple harmonic motion (SHM): The oscillatory motion is said to be simple harmonic, if the
displacement of the particle from the origin varies with time as;
or .
Simple harmonic motion is a periodic motion in which displacement is a sinusoidal function of
time.
Note: The simplest kind of periodic motion is simple harmonic motion.
Analysis of simple harmonic motion:
Consider a particle oscillating back and forth about the origin along between the limits
and as shown.
Figure shows graph of versus which gives the values of displacements as function of time.
Phase: During the periodic motion, the position and velocity of the particle at any time is
determined by the term in cosine function. This quantity is called phase of the motion.
Phase constant (Phase angle):
The value of phase at is and it is called the phase constant or phase angle.
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Chapter-14 OSCILLATIONS
Periodic motion: A motion that repeats itself at regular intervals of time is called periodic motion.
Ex: Motion of planets in solar system, uniform circular motion.
Oscillatory motion: A motion in which a body moves to and fro between two extreme positions
about an equilibrium position.
Ex: boat tossing up and down, piston of a steam engine, motion of simple pendulum.
Equilibrium (Mean) position: It is the position of a body during oscillatory motion at which the
net external force acting on the body is zero.
It is the position, at which if it is at rest, it remains at rest forever.
Oscillations or vibrations: The motion of a body between two extreme positions forms oscillations
or vibrations.
Note: (i) There is no significant difference between oscillations and vibrations. When the frequency
is small we call it oscillation, while the frequency is high we call it vibrations.
(ii) Every oscillatory motion is periodic; but every periodic motion need not be oscillatory.
Importance of oscillatory motion: This motion is basic to physics. In musical instruments we come
across vibrating strings, membranes in drums and diaphragms in telephone and speaker system
vibrate, vibrations of air molecule, vibrations of atoms in solid include oscillatory motion. The
concepts of oscillatory motion are required to understand many physical phenomena listed above.
Description of oscillatory motion: The description of oscillatory motion requires some
fundamental concepts like period, frequency, displacement, amplitude and phase.
Period or Time period (T): The smallest interval of time after which a periodic motion repeats is
called period.
In case of oscillation, the time taken by the body to complete one oscillation is called period. SI unit
of period is .
Frequency ( ): Number of times a periodic motion repeats per unit time is called frequency.
In case of oscillations, number of oscillations per unit time is called frequency. SI unit of frequency
is . oscillation per second.
Note: Relation between period and frequency is given by, ⁄ or ⁄
Displacement (x or y): The term displacement refers to change of physical quantity with time. In
periodic motion displacement may be linear as well as angular.
Linear displacement: The straight line distance travelled by a particle
from its equilibrium position.
Angular displacement: It is the angle through which position vector of the body rotates in a given
time.
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, OSCILLATIONS
Amplitude (A): The maximum displacement of the particle from its equilibrium
position is called amplitude.
Periodic function: Any function which repeats itself after a regular interval of time
is called periodic function.
In periodic motion displacement is periodic function and it can be represented by a mathematical
function of time. The simplest of these functions is given by, .
If is increased by an integral multiple of radian, the value of the function remains same and
is periodic.
( )
Note: (i) In , the term is called angular frequency.
(ii) The function is also periodic.
(iii) The linear combination of both sine and cosine function is also periodic and it is represented
by and it is called Fourier series.
By putting, and
√ ( )
Simple harmonic motion (SHM): The oscillatory motion is said to be simple harmonic, if the
displacement of the particle from the origin varies with time as;
or .
Simple harmonic motion is a periodic motion in which displacement is a sinusoidal function of
time.
Note: The simplest kind of periodic motion is simple harmonic motion.
Analysis of simple harmonic motion:
Consider a particle oscillating back and forth about the origin along between the limits
and as shown.
Figure shows graph of versus which gives the values of displacements as function of time.
Phase: During the periodic motion, the position and velocity of the particle at any time is
determined by the term in cosine function. This quantity is called phase of the motion.
Phase constant (Phase angle):
The value of phase at is and it is called the phase constant or phase angle.
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