Question No.1 Define Vibratory Motion and Give Conditions of A Vibratory Motion?

QUESTION NO.
1
Define vibratory motion and give conditions of a vibratory motion?
Vibratory motion can be defined as:
“When a body moves to and fro about its mean
position along a fixed axis, with equal intervals of time, its motion is known as
vibratory motion”.
Some important conditions for vibratory motion are as under:
1) Restoring force is present in the vibratory motion.
2) To and fro motion of the vibrating body is equal at the specific point.
3) Vibratory body repeats its motion again and again about the same point.
4) Vibratory motion repeats itself in equal interval of time.
QUESTION NO.2
What is wave motion? Describe two experiments to study wave motion?
Wave motion can be defined as,
“Wave motion in a medium is due to the generated
disturbance which causes the constituent particles to repeat its to and fro motion
about its mean position in equal interval of time, and this disturbance is passed over
from one end of the medium to the other”.
Wave motion can be explained by the following two experiments:
EXPERIMENT NO 1
The apparatus require in this experiment is :
 Horizontal surface
 Water tub
 Pencil
 pieces of cardboard
Firstly place a water tub on the horizontal surface and fill it with water. After filling
the tub take a pencil and dip its one end in water and take it out. Now if we rapidly
move the pencil up and down vertically at regular interval of time, then waves are
formed on the surface of the water. Now if we spread the small pieces of cardboard
over the surface of water, we will see that these pieces will move up and down about
their mean positions due to the wave motion.
In this experiment the vibratory motion of the pencil produces the disturbance in the
molecules of water and these molecules starts to create the vibratory motion to their
mean position. Thus this disturbance produces a visible water wave.
Experiment no 2.
The apparatus require in this experiment is:
 A string
 Different colours
 A fixed hook
Take a string and mark it different colours at equal intervals.fix the one end of the
string with a fixed hook with a wall. Now stretch the string by using the other side
with the help of hand. Now move the string up and down to produce the wave. If we
observe carefully the colour full segments then we can see that these segments are
vibrating about their mean position as the wave travels in the string.
It is clear from the above experiment that by creating disturbance at one side of the
string, all the parts of the coloured string start to vibrate to form the wave motion.
BY M.ASIM IQBAL KIANI 1

QUESTION NO.3
Define simple harmonic motion and prove that vibrating motion of mass attached
to spring is SHM?
Simple harmonic motion can be defined as,
“If vibratory motion of a body is such that its acceleration is always directed
towards mean position and its value is directly proportional to its displacement from
equilibrium position then such a vibratory motion is called simple harmonic motion.”
VIBRATING MOTION OF MASS ATTACHED TO SPRING IS SHM

Let us consider a mass ‘m’ attached with one side of a spring placed on a horizontal
surface whereas the other side of the spring is attached with a fixed hook.
When the mass is in equilibrium then there is no extension in the spring and position
of mass is called mean position / equilibrium position.
When we apply external force Fext the spring extends. This extension is
denoted by ‘x’ and due to this force the position of the mass changes from O to A.
According to hook’s law,
Fext ∝ x
Fext = Kx (1)
Here k is spring constant.

F ext
K=
x
This equation shows that the ratio of the external force acting on a spring to the
increase in its length is called the spring constant. Its unit is Nm -1.
When spring is released then external force becomes absent and spring comes to its
original shape. This is called restoring force. During the motion of mass ‘m’ if the
displacement is ‘x’ then the restoring force will be opposite to the external force so,
F = -Kx (2)
Now if the mass ‘m’ is let free, it starts moving towards the point ‘O’. By using the
Newton’s 2nd law of motion, acceleration ‘a’ of the mass ‘m’ can be found as,
F
a=
m
F
a = const.
m
F
a=
m
From equation 2, we get the value of F
−kx
a=
m
Since k/m is constant, therefore
a∝ -x
This shows that the acceleration of the body is directly proportional to displacement
from mean position and in opposite direction to the displacement due to negative
sign. Due to motion of mass towards the mean positions the value of x decreases. In
this way the value of acceleration also decreases and finally becomes zero when
mass reaches at mean position.

The velocity of mass becomes maximum when it is at mean position. Due to inertia,
the mass continues its motion even when its acceleration is zero at mean position.
So mass moves away from the mean position in opposite direction. This decrease
the length of spring. The restoring force is in opposite direction and is still towards
mean position. The acceleration is produced in opposite direction of motion of mass.
So its velocity decreases and comes to zero and mass stops for a moment at
position A’. Due to this acceleration the motion of the mass is reversed and it moves
towards mean position again. Due to inertia mass crosses the mean position and
moves from O to A. This process repeats again and again and mass vibrates
between points A and A’.
The motion of a mass attached to a spring is known as simple harmonic motion.
Mathematically, it can be proved that the time period ‘T’ of the simple Harmonic
Motion of a mass attached to a spring can be given by the following equation.
m
T =2 Ω
k √
QUESTION NO.4
Define the following terms:
Displacement, amplitude, frequency, time period?
Displacement:
The distance of vibrating body from mean position in a particular distance is called
displacement. Its unit is meter (m).
Amplitude:
The maximum possible displacement from mean to extreme position is called amplitude.
Its unit is also meter (m).
Frequency:
The number of vibrations completed by the vibrating body in one second is called its
frequency. Its unit is vibrations per second also known as hertz.
Time period:
The time required to complete one vibration is called time period. Its unit is second.
QUESTION NO.4
Describe simple pendulum?
A simple pendulum consists of a single isolated bob suspended from
a frictionless support by a light inextensible string.
The point ‘O’ is called mean position where the bob becomes
stationary. If the bob is disturbed from its mean position and then
released then it becomes to vibrate about its mean positions
between points ‘A’ and ‘B’. Then bob begins to move from ‘A’ to ‘B’
and then from ‘B’ to ‘A’. And repeats this again and again.
The velocity of bob becomes maximum at the mean position ‘O’ and
this velocity becomes zero at the extreme positions ‘A’ and ‘B’. When
bob moves from ‘A’ to ‘O’ then its acceleration also along A’ to ‘O’
and speed also increases. When bob moves from ‘O’ to ‘B’ its velocity A
decreases and acceleration is in opposite direction of its motion. B

This shows that acceleration of bob is always directed towards mean position. And its value is zero
when it is not at the mean position and it increases with the increase of its displacement from the
mean position. So motion of bob of pendulum is simple harmonic motion.
Whereas the time period of simple pendulum is
l
Where as; l = length of pendulum

T =2 Ω
√ g
g = gravitational acceleration
potential energy will be minimum and kinetic energy will be maximum at position ‘O’ because the
bob is at lowest position of the motion.
And potential energy will be maximum and kinetic energy will be minimum at positions ‘A’ and ‘B’
because at these points the bob will be at highest position. In between the extreme and mean
positions at any point the energy of bob is partly potential and partly kinetic. However during
vibration the total energy remains constant.
QUESTION NO.5
Write down the characteristics of SHM?
Some important characteristics of SHM are as follows:
1) A body executing simple harmonic motion always vibrates about its position of equilibrium.
2) Its acceleration is always directed towards its mean position.
3) Its acceleration is directly proportional to its displacement from the mean position.
4) Its acceleration is zero at the mean position.
5) Its acceleration is maximum at the extreme positions.
6) Its velocity is maximum at the mean position.
7) Its velocity is zero on the extreme positions.
QUESTION NO.6
What is a wave? Describe its types and define them.
Waves are produced in a medium due to such a disturbance which causes the particles of the
medium to exhibit SHM about their mean position after a particular interval of time. In this way the
disturbance is transmitted from one part of medium to the other in the form of waves.
Examples of waves:
Waves produced on the surface of the water
Waves produced in a stretched string.
TYPES OF WAVES
There are two types of waves which are as under:
1-MECHANICAL WAVES
The waves which require medium for their production are known as Mechanical Waves.
Examples:
 Waves produced on the surface of the water.
 Waves produced in a stretched string.
In above two examples the water and the string are the mediums by which the waves are produced.
2-Electromagnetic Waves
The waves which do not require the medium for their production are known as
electromagnetic waves.
Examples:
 Radio waves
 Television waves
 X-rays
 Heat waves
 Light waves
QUESTION NO.7
Describe the types of Mechanical Waves?
There are two types of the mechanical waves:
I) Transverse waves
Transverse waves are such waves in which the particles of the medium vibrate perpendicular to the
direction of propagation of the wave.
II) Compressional or longitudinal waves

Question No.1 Define Vibratory Motion and Give Conditions of A Vibratory Motion?

Uploaded by

Copyright:

Available Formats

Question No.1 Define Vibratory Motion and Give Conditions of A Vibratory Motion?

Uploaded by

Document Information

Original Description:

Original Title

Copyright

Available Formats

Share this document

Share or Embed Document

Sharing Options

Did you find this document useful?

Is this content inappropriate?

Copyright:

Available Formats

Question No.1 Define Vibratory Motion and Give Conditions of A Vibratory Motion?

Uploaded by

Copyright:

Available Formats

QUESTION NO.

BY M.ASIM IQBAL KIANI 1

VIBRATING MOTION OF MASS ATTACHED TO SPRING IS SHM

Here k is spring constant.

BY M.ASIM IQBAL KIANI 2

BY M.ASIM IQBAL KIANI 3

Where as; l = length of pendulum

BY M.ASIM IQBAL KIANI 5

You might also like