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AITAZAZ AHSAN 1

AITAZAZ AHSAN 10-ME-04

To observe the influence of variations of mass on bifilar suspension.

Apparatus:

Mechanical vibration apparatus Bifilar suspension Masses Stop watch Level gauge

Bifilar suspension

Procedure:

Set up the apparatus making sure that the two threads are parallel. Weigh the mass of rod with the help of digital weight balance. Without adding any mass, displace the rod (mass of rod=400g) in the horizontal plane and

release it.

Record the time for 20 oscillations (T20) by using a stop watch and hence calculate theperiod (T) by using the formula

o T=T20/20 Add a mass of100g, again record time for 20 oscillations (T20) and hence calculate the

period (T).

Repeat above procedure by adding a mass of 300g.Observations and calculations

SR# Length of

bifilarsuspension

mm

Mass of bifilar

suspensiongm

T20 secs T=T20/20 secs

1 580 400 22.18 1.109

2 580 500 21.91 1.09

3 580 800 21.97 1.09

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AITAZAZ AHSAN 2


Precautions

Apply smaller displacements Time of vibrations should be noted correctly There should be no disturbing factor

Result:

There is no difference in variation of mass on bifilar suspension as time period remain same.

To Find Spring Constant k

Apparatus:

Mechanical vibration apparatus Masses Verneir caliper Steel rule Stop watch Springs

0

100

200

300

400

500

600

700

1.085 1.09 1.095 1.1 1.105 1.11 1.115

length of bifilar

suspension mm

time period t secs

graph between length of bifilar suspension &

time period

Series1

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AITAZAZ AHSAN 3


Procedure:

Set the apparatus according to the experiment Hang two springs at a distance on mechanical vibration apparatus Now hang two different masses on the spring As the masses are hanged elongation will produce in the springs Measure the elongation in the springs From these elongations calculate the spring constant by formula

k=m2-m1/x2-x1(g)

Repeat experiment thrice

Observations and calculations

Sr# Mass m 1gm.

Mass m2gm.

Elongation

x1mm

Elongation x2mm

k=m2-

m1/x2-x1

(g)

1 0 100 65 66 98

2 100 200 66 68 49

3

Precautions:

Do not overload the springs otherwise it will cause permanent elongation Do not add masses simultaneously measure elongations very carefully

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AITAZAZ AHSAN 4


To find the natural frequency of an un damped free vibration systems using mechanical

vibration apparatus. Compare theoretical and experimental results.

Apparatus:

Beam Spring Stud Nut Plotter Pen Pen holder

Theory:

We know

Disturbing torque= -Restoring forceJo.. = -Fa

Jo.. + Fa=0Where F=kx

Jo=ML2/3

ML2

/3+(kx)a=0From figurex=asin

x=aML2.. /3+k (a) a=0

ML2.. /3+a2k=0

Dividing by ML2/3 to remove coefficient of ..

+ a2k/ ML2/3=0..+ 3a2k/ ML2=0

Therefore by comparing 2n=3a2k/ ML2

n= 3a2k/ ML2

=2f

fn=1/2(3ka2/ml2)2

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AITAZAZ AHSAN 5


Procedure:

Set the apparatus and note down the values of length of beam (L), mass of beam (M)and stiffness of spring (K) which are constant.

Note down the value of distance a i.e. position of spring. Set the plotter. Displace the beam vertically down and start the plotter and stop watch just at the

moment the beam is released.

Note down the time and count the number of waves on plotter. Calculate the theoretical value of natural frequency by using formula, Calculate the experimental value of natural frequency by using formula

fn=W/T

Where,

W is no. of waves on plotter.

T is total time.

Calculate the difference of experimental and theoretical value of natural frequency of anun damped free vibration system.

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AITAZAZ AHSAN 6


Observations and calculations

Precautions

Calculate the number waves very carefully Start the stop watch as the plotter start plotting waves

Result

Comparison of theoretical and experimental values of natural frequency of an un damped free

vibration system shows little difference which may be due to personal error in taking readings and

natural frequency an un damped free vibration system can be changed by changing the position of

the spring.

Sr

No.

L

(mm)

M

(kg)

K

(N/mm)

a

(mm)

fn

=1/23ka2/ML2

(Hz)

No. of

waveson

plotter

(W)

Total

TimeT

(sec)

fn=W/T

(Hz )

Difference

1. 730 1.68 750 650 5.186 4.5 0.97 4.639 0.547

2. 730 1.68 750 600 4.787 6.5 1.66 3.916 0.871

3. 730 1.68 750 550 4.388 9 2.50 3.6 0.788

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AITAZAZ AHSAN 7


Determination of Natural Frequencies of Free Damped Oscillations

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AITAZAZ AHSAN 8


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AITAZAZ AHSAN 9


Torsional Vibrations

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AITAZAZ AHSAN 10


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AITAZAZ AHSAN 11


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AITAZAZ AHSAN 12


Forced Vibrations with Negligible Damping

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AITAZAZ AHSAN 13


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AITAZAZ AHSAN 14


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AITAZAZ AHSAN 15


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AITAZAZ AHSAN 16


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AITAZAZ AHSAN 17


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