# dynamics lab manual by rjohnpeter

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```									                  EINSTEIN
COLLEGE OF ENGINEERING
Sir.C.V.Raman Nagar, Tirunelveli-12

Department of Mechanical Engineering

ME57- Dynamics lab

Name              : ………………………………………

Reg No            : ………………………………………

Branch            : ………………………………………

Year & Semester   : ………………………………………
Sub Code: ME57 Dynamics Lab

Sl.No    Date of        Name of the Experiment           Page    Marks     Staff    Remarks

Experiment                                       No               Initial

1                   Determination of speed and
sensitivity for watt governor

2                   Determination of speed and
sensitivity for proell governor

3                   Determination of speed and
sensitivity for porter governor

Determination of speed and
4                   sensitivity for hardnell governor

5                   Determination of moment of
inertia by oscillation method

6
Cam study model

7
Determination of whirling speed
of shaft

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Sub Code: ME57 Dynamics Lab

8    Balancing of rotating mass

Verification of gyroscopic
9        relation

10   Study on balancing of
reciprocating mass

11   Determination of natural
frequency in vibrating table

Multi degree of freedom
suspension
12

Determination of natural
13   frequency of transverse
vibration

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Sub Code: ME57 Dynamics Lab

DETERMINATION OF SPEED AND SENSITIVITY FOR
WATT GOVERNOR
DATE:
EXP NO: 1
Aim:
To determine the speed and sensitivity of the Watt Governor.
Apparatus Required:
1.Watt governor set up.
2.tachometer
3.dimmer
Formula:

1. Speed, N = √(895/h) rpm h-sleeve lift
2. Sensitivity= N/N2-N1       N2-Maximum speed        N1-Minimum speed
N-Mean speed
Procedure:
1. The watt governor assembly is mounted over the spindle.
2. The motor is started and speed is adjusted. Speed is measured with the help of
tachometer.
3. Due to this centrifugal force the sleeve will be rise, the speed and the sleeve height are
noted.
4. By using the formula the speed of the governor is calculated.
5. The experiment is repeated at different speed and force.

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Sub Code: ME57 Dynamics Lab

Tabulation:

Sl.no   Motor speed (rpm)   Sleeve lift (h)   Governor speed (N)
(mm)                (rpm)

Calculation:

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Questions:
1) What is watt governor?
2) Difference between function of flywheel and governor?
3) What are the limitations of watt governor?
4) Explain working principle of watt governor?
5) What is height of a watt governor?

Result:
At different motor speed the sleeve lift are noted and corresponding governor speed and
sensitivity are calculated.

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Sub Code: ME57 Dynamics Lab

DETERMINATION OF SPEED AND SENSITIVITY FOR
PROELL GOVERNOR
Date:
Exp No:2
Aim:
To determine the speed and sensitivity of the proell Governor.

Apparatus Required:
1.Proell governor.
2.Tachometer.
3.Dimmer.

Formula:

N = √ FM/BM x (m+M/m) x 895/h.
Where,
FM/BM-proell link ratio =0.57. M-mass of the sleeve assembly=2.25kg
m-mass of the ball = 0.092 kg. h-sleeve lift

Sensitivity=N/N2-N1             N2-Maximum speed             N1-Minimum speed
N-Mean speed
Procedure:
1. The proell governor assembly is mounted over the spindle.
2. The motor is started and speed is adjusted. Speed is measured with the help of
tachometer.
3. Due to this centrifugal force the sleeve will be rise, the speed and the sleeve height are
noted.
4. By using the formula the speed of the governor is calculated.
5. The experiment is repeated at different speed and force.

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Sub Code: ME57 Dynamics Lab

Tabulation:

Sl.NO     MOTOR       SLEEVE LIFT(h)   GOVERNORSPEED( N)
SPEED (rpm)       (mm)                rpm

Calculation:

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Sub Code: ME57 Dynamics Lab

Questions:
1) Explain proell governor working principle?
2) What is controlling force?
3) Explain the term “power of governor”?
4) Explain the term “Hunting of governor”?
5) Why is it that the speed ranges of a proell governor less than that of porter governor?

Result:
At different motor speed the sleeve lift are noted and corresponding governor speed and
sensitivity are calculated.
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Sub Code: ME57 Dynamics Lab

DETERMINATION OF SPEED AND SENSITIVITY FOR
PORTER GOVERNOR
Date:
Exp No:3
Aim:
To determine the speed and sensitivity of the porter governor.
Apparatus required:
1. Porter governor.
2. Tachometer.
3. Dimmer.
Formula:

1. Governor speed n = √ (m+M/m) * (895/h) rpm.
M-mass of the sleeve assembly =2.25 kg     h-sleeve lift
m-mass of the each ball=0.225 kg
2. Sensitivity= N/N2-N1          N-Mean speed       N2-Maximum speed
N1-Minimum speed
Procedure:
1. The porter governor assembly is mounted over the spindle.
2. The motor is started and speed is adjusted. Speed is measured with the help of
tachometer.
3. Due to this centrifugal force the sleeve will be rise, the speed and the sleeve height are
noted.
4. By using the formula the speed of the governor is calculated.
5. The experiment is repeated at different speed and force.

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Sub Code: ME57 Dynamics Lab

Tabulation:

S.No                        Sleeve Lift (h)   Governor speed (N)
Motor Speed (rpm)
(mm)                (rpm)

Calculation:

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Sub Code: ME57 Dynamics Lab

Question:
1) Explain working principle of porter governor?
2) Explain the terms stable and unstable of governor?
3) What is spring controlled governor?
4) Define power of porter governor?
5) What is effort of porter governor?

Result:
At different motor speed the sleeve lift are noted and corresponding governor speed and
sensitivity are calculated.
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Sub Code: ME57 Dynamics Lab

DETERMINATION OF SPEED AND SENSITIVITY FOR
HART NELL GOVERNOR
Date:
Exp No:4
Aim:
To determine the speed and sensitivity of the Hart Nell governor.

Apparatus Required:
1. Hart Nell governor
2. Tachometer.
3. Dimmer.
Formula:

1. Governor speed n = √ (m+M/m) * (895/h) rpm.
M-mass of the sleeve assembly =2.25 kg       h-sleeve lift
m-mass of the each ball=0.225 kg

2. Sensitivity= N/N2-N1        N-Mean speed         N2-Maximum speed
N1-Minimum speed
Procedure:
1. The porter governor assembly is mounted over the spindle.
2. The motor is started and speed is adjusted. Speed is measured with the help of
tachometer.
3. Due to this centrifugal force the sleeve will be rise, the speed and the sleeve height are
noted.
4. By using the formula the speed of the governor is calculated.
5. The experiment is repeated at different speed and force.

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Sub Code: ME57 Dynamics Lab

Tabulation:

Sl.No     Motor Speed   Sleeve Lift (h)   Governor speed (N)
(rpm)           (mm)                (rpm)

Calculation:

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Sub Code: ME57 Dynamics Lab

Question:
1) Compare gravity-controlled and spring controlled governor?
2) Working principle of hartnell governor?
3) What is sensitiveness of a governor?
4) Types of spring controlled governor?
5) Define centrifugal governor?

Result:
At different motor speed the sleeve lift are noted and corresponding governor speed and
sensitivity are calculated.

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Sub Code: ME57 Dynamics Lab

DETERMINATION OF MOMENT OF INERTIA
BY OSCILATION
Date:
Exp No:5
Aim:
To determine the moment of inertia by oscillation method.
Apparatus Required:
1. Fly wheel          3. Main Frame
2. Chucks             4. Connecting rod.
Formula Used:
1. Polar moment of inertia (J) = /32xd4 m4
d-dia of the connecting rod ends
2. Torsional Rigidity (q) =GJ/l N-M
G-Modulus of rigidity of material=0.79x1011
l-Length of the connecting rod
3. Moment of Inertia (I) =4q/ 2f2 =4qt2p/   2
kg-m2
Procedure:
1. The connecting rod for which the moment of inertia is to be found is fixed the inner
diameter of the rod is measured by various points.
2. The mean diameter is taken as the diameter of the rod.
3. The rod is fixed at both at the top of the chuck and the flywheel and the length
between two points is measured then a small twist is given to the flywheel and is
released.
4. The time taken for the 5 oscillation is noted in the tabular column.
5. The same experiment is repeated for various lengths and at different diameter the
experiment is done by adding the weight of flywheel and the reading are noted
down.

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Sub Code: ME57 Dynamics Lab

Tabulation:

Length of    Diameter of    Moment of
rod           rod          inertia
Sl.no       End      N    T      tp =
position                t/n    (mm)           (mm)          Kg-m2
(sec)

Calculation:

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Sub Code: ME57 Dynamics Lab

Questions:
1) What is polar moment of inertia?
2) What is big end & small end?
3) What is the function of connecting rod?
4) What is “co-efficient of fluctuation of speed”?
5) What is mass moment of inertia?

Result:
Thus the moment of inertia of the given rod is calculated and tabulated.

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Sub Code: ME57 Dynamics Lab

CAM STUDY MODEL
Date:
Exp No:6
AIM:
To draw the displacement diagram for various cam profile and various followers.
APPARATUS REQUIRED:
1) Experimental setup 2) Flat, Roller, Knife edge follower 3) Cams

PROCEDURE:
1.Taka a paper of size 40cm x 15cm, use scale for x-axis as 1cm = 10 of rotation of cam.
2.Take height of lift as10cm.
3. Plot displacement diagram for given cam profile.
4.Fit graph paper on drum. set ‘0’ as a starting point to lift.
5.Give gradual rotation to complot displacement diagram on graph.
6.Compare solution obtained by graphical. Do this for other cam profile and follower.

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Sub Code: ME57 Dynamics Lab

Tabulation:

Roller follower           Mushroom follower        Knife edge follower

Degree       Displacement   Degree    Displacement   Degree     Displacement

Calculation:

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Sub Code: ME57 Dynamics Lab

Question:
1) Classification of cams and followers?
2) Types of follower motion?
3) Explain cam function?
4) Define pressure angle?
5) Explain the term “maximum fluctuation of energy”?

RESULT:
Thus the displacement diagrams are drawn for the given follower and various cams.

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Sub Code: ME57 Dynamics Lab

DETERMINATION OF WHIRLING SPEED
OF THE SHAFT
Date:
Exp No:7

Aim:
To determine the whirling speed of a shaft at various supporting condition.

Apparatus required:
1. Whirling shaft apparatus    2. Various support and bearings.
3. Tachometer      4. Vernier caliper   5. Steel rule

Formula Used:
1. Deflection =h2-h1 cm
h1-minimum deflection, h2-maximum deflection

2. Whirling speed=1/2 √g/ rpm
g-gravity 9.81

Procedure:
1. First fixing the arrangement, are selected.
2. The shafts are fixed firmly on the suitable bearing and tighten it.
3. Then the motor is switched on and speed of the motor is increased.
4. The modes of shaft vibration are noted. By using the formula the frequency at various
vibrations calculated.
5. Same procedure repeated using various diameter (4,6 and 8mm) of shaft.

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Sub Code: ME57 Dynamics Lab

Tabulation:

Sl.No    Diameter   Length     Speed   Weight of the shaft per unit   Whirling speed
of shaft   of shaft                   length (w)
(N)                                       (rpm)
(mm)    (cm)               h1       h2          δ
rpm
(cm)     (cm)        (cm)

Calcultion:

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Sub Code: ME57 Dynamics Lab

Questions:
1) What is whirling speed?
2) Define amplitude?
3) Define resonance?
4) What is Damper & types of damper?
5) Define degree of freedom?

Result:
Thus the whirling speed of the various shaft at various end condition are calculated.

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Sub Code: ME57 Dynamics Lab

BALANCING OF ROTATING MASS
Date:
Exp No:8

Aim:
To verify the balancing using the rotating machine element.

Apparatus required:
1. Balancing rotary system      2. Masses.

Procedure:

1.To order of the basic operation involved with respect to static balancing as following
2.Then the mass should be fixed in one side of the stud and its angle to be adjusted with the
help of angular scale and its radil can be corrected with the help of vernier caliper.
3.Angular displacement between the masses Is calculated by force diagram through known
4.Fix the masses to the calculated angular displacement using angular scale.
5.Now switch on the motor.
6.By changing the sped of the motor, check it out for vibration for running
7.Add by changing the mass with different radil and find out the angular displacement among
the mass for balancing the system

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Sub Code: ME57 Dynamics Lab

Tabulation:

Sl.No        Plane   A   B    C             D

Mass

θ

Calculation:

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Sub Code: ME57 Dynamics Lab

Question:
1) What is meant by balancing?
2) What are the types of balancing?
3) What is reference plane?
4) What is turning moment diagram?
5) What is swaying couple?

Result:
Thus the Balancing Of Rotating Machine Was Verified.

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Sub Code: ME57 Dynamics Lab

VERIFICATION OF GYROSCOPIC RELATION
Date:
Exp No:9

Aim:
To analysis the gyroscopic effect using the test setup and verify the gyroscopic rules of
plane disc.

Apparatus Required:
1. Gyroscopic setup. 2. Weight     3. Tachometer

Technical Data:
1.Rotor diameter (d) = 30 cm.
2.Rotor thickness (t) = 8cm.
3.Distance of weight pan bolt centre to disc center (l) = 260 mm.
4.Weight of the rotor = 7kg.

Formula Used:
1. Precision ratio (wp) = 2 n/60 rad/ sec.
2. Angular velocity (w)=dØ/dt X /180 rad/sec
dØ-change in degree            dt-time taken in sec

3. Gyroscopic effect (c) = I.ω.ωP
4. Torque, t = wxr
Where,
w = weight of the rotor.
r = distance between weight pan centre to disc centre.
5. I = mr2/2 Kg-m2.           m-mass of the rotor kg

6. Percentage of error = (T-C)/T X 100.

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Sub Code: ME57 Dynamics Lab

Procedure:
1.Switch on the supply.
2.Set the require speed of the regulator as constant.
4.Angle of precision d i.e. Measured.
5.Loose the lock screw, start the stop watch and note down.
6.Watch the particular interval and time.
8.Repeat the equipment maintaining load as constant and varying the speed.
9.Do the calculation.

Tabulation:

Speed Of Disc (rpm)     Added weight                 dθ                       dt
(gm)                 (degree)                  (sec)

Angular velocity     Applied couple on      Precision ratio         Gyroscopic Effect c
tachometer (Tact)

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Sub Code: ME57 Dynamics Lab

Calculation:

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Sub Code: ME57 Dynamics Lab

Question:
1)   Define gyroscopic couple?
2)   What is gyroscopic torque?
3)   Define Axis of precession & Axis of spinning
4)   Explain gyroscopic Effect on naval ship?
5)   Explain gyroscopic effect on aero plane?

Result:
Thus the Gyroscopic relation was verified.

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Sub Code: ME57 Dynamics Lab

STUDY ON BALANCING OF RECIPROCATING MASS

Date:
Exp No:10

Aim:
To study the behavior of vibration due to the unbalanced mass in reciprocating parts.

Apparatus required:
Balancing of reciprocating mass system masses.

Procedure:

1.Initially all weights and bolts are removed then the motor is started. The speed of the motor is
increased due to the unbalanced masses, the vibration will be created. The vibration Is
observed.
2.The speed is noted down. Now the speed is increased and the vibrations are all so noted
down. The motor is switched off then some weights added on the piston top. The weights
may be added on the piston top. The weights may be added either eccentrically (or) co-
axially. Now the motor is started the vibrations are observed at the tested speed noted in the
previous case. If still the vibration are observed. One of the following has to be done to
eliminate the unbalance forces
3.Some weights are added in opposites direction of crank and the engine run and the vibration,
are observed at the tested speed.
4.Combination of both the above cases. The speeds, the weight added on piston, diameter at
which the weights are added are noted down at different case.

Result:

The vibrations due the unbalanced forces in the reciprocating masses are studied.

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Sub Code: ME57 Dynamics Lab

DETERMINATION OF NATURAL FREQUENCY
USING VIBRATING TABLE
Date:
Exp No:11
Aim:
To find natural frequency of free vibration and forced vibration using vibration table.
Apparatus Required:
1) Spring 2) mass 3) damper 4) stopwatch       5) steel rule.

Formula Used:
Natural Frequency fn=N/T Hz
N-No of oscillation        T=Time period of 5 oscillations in sec

Procedure:
Free Vibration:
1) Remove the damper from the experimental setup.
2) Then strike the beam by taken 5 oscillation time required.
3) Repeat the procedure for different length of beam to adjust the beam set up.
Forced Vibration:
1) Fit the spring, mass damper in proper position note down the spring stiffness, mass of
the beam, length of the beam from one tunion point and measure the exciter mass.
2) The electrical motor is switched ON, using stop watch note down 5 oscillation time
for small jerk.
3) Then repeat the procedure for different length of beam.

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Sub Code: ME57 Dynamics Lab

Tabulation:
Free vibration:

Time required to
complete one set of
Exciter      No of             oscillation         Time      Frequency
position   oscillation                             period
Sl.No     Vibration                                     (sec)             ’T’        (Hz)

Forced Vibration:

Time
period(T)
S.No     Vibration     Exciter        No of                          Frequency (Hz)     Speed
position     oscillation          (sec)                          (rpm)

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Sub Code: ME57 Dynamics Lab

Calculation:

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Sub Code: ME57 Dynamics Lab

Question:
1) What are different types of vibrating motions?
2) Define free vibration& forced vibration?
3) What is damping?
4) Define D’Alemberts principle?
5) Define critical speed?

Result:
Thus the natural frequency of free and forced vibration using vibrating tale was found.

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Sub Code: ME57 Dynamics Lab

MULTI DEGREE OF FREEDOM SUSPENSON
Date:
Exp No:12

Aim:
To find out the mass moment of inertia of any irregular section.

Apparatus required:
1) Bifilar and trifler setup    2) stopwatch
3) Different weight of cycle    4) steel rule

Formula Used:
Bifiller:
1) Natural Frequency fn=N/T Hz

2) Radius of Gyration k=1/2 fnx√g.ab/l
3) Moment of Inertia I=mk2 kg-m2
Where,
N-No of oscillation                   ab-Distance between two nodes
Fn-Natural Frequency in Hz             l-length of the thread
T-Time taken for 5 oscillations in sec k-Radius of gyration
M-mass of the bifiller plate
Trifiller:

1) Radius of gyration k=1/2 fnx√g.r2/l
2) Moment of inertia I=mk2 kg-m2
Where,
r-Radius of the Trifiller     m-mass of the trifiller g-Gravity (9.81)

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Sub Code: ME57 Dynamics Lab

Procedure:
1) Select either of bifilar (or) trifler plates.
2) With the help of spring chucks lighter at tops.
3) Adjust the length of spring to descry the value (or) measure length on it.
4) Give small horizontal twist at the same time start the stop watch and note down time
required for five (or) ten oscillation.
5) Repeat the experiment by adding weight and checking length.
Tabulation:

of                   of Inertia
S.NO    Types of        Self       No. of     Time        weight     gyration    Natural
Suspensio      weight      oscilla    Taken       added         K       frequency        I
n                       tion
(kg)                    sec           (gm)     (m)        (fn)       (Kg-m2)
Hz

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Sub Code: ME57 Dynamics Lab

Calculation:

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Sub Code: ME57 Dynamics Lab

Questions:
1) Explain laws of motion?
2) What is free body diagram?
3) What is static& dynamic force Analysis?
4) Define simple harmonic motion?
5) Define crank pin effort & piston effort?

Result:
Thus the MI of irregular section find out.

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Sub Code: ME57 Dynamics Lab

DETERMINATION OF NATURAL FREQUENCY OF TRANSVERE VIBRATION
Date:
Exp No:13
Aim:
To determine the natural frequency of free transverse vibration due to uniformly distrusted load
and concentrated load over a simply supported shaft.

Apparatus Required:
1. Shaft    2. Stop watch    3. Weight     4. Transverse vibration system.

Formula Used:
Simply supported Beam:

1. Uniform Distributed Load Frequency (fn) =0.571/√

2. Point load Frequency (fn) =0.4985/√

3. Varying load Frequency (fn) =0.4985/√
Cantilever Beam:

1. Cantilever Beam Frequency (fn) = (1/2 ) x√g/
g-Gravity            -Deflection.
Procedure:
1. First proper lubrication is done for the bearing.
2. The given beam is fitted into the slots of Turn ion bearings and they are tightened.
uniformly or concentrated.
Then the beam is given a swing and starts oscillating.
4. The time taken for five oscillations noted down.
5. The experiment is repeated for various types of loads and the types of beams.

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Sub Code: ME57 Dynamics Lab

Tabulation:

FREQUENCY
(fn) Hz

VARIYING

M

VARIYING
DEFEL                  DEFEL       TIM     DEFEL
TIME                                   TIME
CTION                  CTION       E       CTION

UDL
(sec)                                  (sec)
(cm)                   (cm)        (sec)   (cm)

Observation:
1) Mass of the each weight (m)=158 gm
2) Length of the cantilever beam=235mm
Calculation:

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Questions:
1) Define “Logarithmic Decrement”?
2) Define” under damped”, “over damped” vibrations?
3) What is critical speed?
4) Define natural frequency?
5) What do you understand by whirling motion?

Result:
The natural frequency of transverse vibration due to UDL and concentrated load over a
simply supported shaft is calculated and is compared with experimental value.
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