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MAHENDRA ENGINEERING COLLEGE

(Autonomous) Mahendhirapuri, Mallasamudram, Namakkal DT -637 503.

DEPARTMENT OF MECHANICAL ENGINEERING

PRACTICAL WORKBOOK

ME13L52- KINEMATICS & DYNAMICS LABORATORY

NAME OF THE STUDENT : ……………………

REGISTER NO : ……………………

DEPARTMENT : ……………………

YEAR/SEMESTER : ……………………

BATCH : ……………………

2

TABLE OF CONTENTS

1) Syllabus

2) General Instruction

3) List of Experiments / Index

3

SYLLABUS

MAHENDRA ENGINEERING COLLEGE (AUTONOMOUS)

SYLLABUS -R 2013

SEMESTER - IV

Course Code Course Name Hours / Week Credit

L T P C

KINEMATICS & DYNAMICS

LABORATORY

0 0 3 2

Objectives

To supplement the principles learnt in kinematics and Dynamics of Machinery and to

understand how certain measuring devices are used for dynamic testing.

.

LIST OF EXPERIMENTS

1. Kinematics of Four Bar Mechanisms- Slider Crank and Crank Rocker Mechanism-Determination of velocity

and acceleration.

2. Kinematics of universal joints (single and double)-Determination of velocity and acceleration.

3. Kinematics of Gear trains-Simple, Compound, Epi-cyclic and Differential: Determination of velocity ratio

and Torque.

4. Governors-Determination of range sensitivity, effort etc., for any one of Governors - Proell Governor.

5. Motorized gyroscope-Verification of laws- Determination of gyroscopic couple.

6. Whirling of shafts – Determination of critical speeds of shafts with concentrated loads.

7. Balancing of rotating and reciprocating masses.

8. Determination of Mass moment of inertia by oscillation method for connecting rod.

9. Vibration system- Spring mass system- Determination of damping co-efficient of single degree of freedom

system.

10. Determination of torsional frequencies for compound pendulum and flywheel system with lumped Moment

of inertia.

11. Cam – Determination of jump speed and profile of the cam.

12. Vibrating Table – Vibration Measurement.

Quantity: One each. Total Number of Periods: 45

4

GENERAL INSTRUCTIONS

Lab Safety Do's and Don’ts for Students

Life threatening injuries can happen in the laboratory. For that reason, students need to be

informed of the correct way to act and things to do in the laboratory. The following is a safety

checklist that can be used as a handout to students to acquaint them with the safety do’s and

don’ts in the laboratory.

Don’ts

Do not engage in practical jokes or boisterous conduct in the laboratory.

Never run in the laboratory.

The use of personal audio or video equipment is prohibited in the laboratory.

The performance of unauthorized experiments is strictly forbidden.

Never work in the laboratory without the supervision of a teacher.

Never leave experiments while in progress.

Never attempt to catch a falling object.

Never fill a pipette using mouth suction. Always use a pipetting device.

Do not remove any equipment from the laboratory.

Do’s

Know emergency procedures.

Always perform the experiments or work precisely as directed by the teacher.

Immediately report any spills, accidents, or injuries to a teacher.

Make sure no flammable solvents are in the surrounding area when lighting a flame.

Coats, bags, and other personal items must be stored in designated areas, not on the

bench tops or in the aisle ways.

Notify your teacher of any sensitivities that you may have to particular chemicals if

known.

Keep the floor clear of all objects (e.g., ice, small objects, and spilled liquids).

Wear shoes that adequately cover the whole foot; low-heeled shoes with non-slip soles

are preferable. Do not wear sandals, open-toed shoes

5

INDEX

Ex.No Date Description Marks

Awarded

Signature of

the Staff

6

TABULATION:

S.No Crank

angle

Distance

between

crank to

slider

(exp)

x

Angle

between

slider &

connecting

rod

Ø

Velocity

of slider

(exp)

VP

Angular

velocity of

connecting

rod

ωc

Velocity

of slider

VP

Angular

velocity of

connecting

rod

(Theo)

ωc

Distance

between

crank &

centre

slide

crank

(Theo)

x

deg cm deg Cm/s rad/s Cm/s Rad/s cm

MODEL CALCULATION:

7

KINEMATIC CHAIN OF FOUR BAR MECHANISM

Exp No:

Date:

Aim: To determine the angular velocity ratio for various angular position as crank for the given link

size.

Apparatus required:

Experimental setup

Lens

Align key

Formula:

θ3 =tan-1{(r4sin θ4-r2sin θ2)/(r1-r2cos θ2+r4cos θ4)}

ω4/ω2=r2sin(θ3- θ2)/r4sin(θ3- θ4)

ω3/ω2= r2sin(θ4- θ2)/r4sin(θ3- θ4)

Where

θ3=coupler rod angle

θ2=crank angle

θ4=rocker arm angle

r2=length of crank

r3=length of coupler rod

r4=length of rocker arm

ω2= angular velocity of crank

ω3=angular velocity of coupler rod

ω4= angular velocity of rocker arm

Testing procedure:

l. Check the position of the grub screw in crank.

2. And also check the position of the coupler and Rocker.

3. Check the Angular position of crank and Rocker can be measured to an

accuracy of 0.1o.

Description:

The experimental set consists of a four bar mechanism model having the following features.

(1) Two links are fixed on to a board. The distance between the pivots are considered as length of

fixed link 1.

(2) Each moving link is telescopic type and its length can be varied by grub screw provided.

(3) Hinges are provided with ball bearings to reduce error due to clearance.

(4) Angular position of links 2 (crank) and 4 (rocker) can be measured to a resolution of 0.1o by

venire protractors.

(5) The links are in two planes so that complete rotation of crank is possible.

8

MODEL CALCULATION:

9

Experimental procedure

6. Links are numbered in anti clockwise starting with fixed link as 1. Ensure that

0z is zero when link 2 coincided with link 1.

7. Measure value of 0+ for various values of 02, 0, l0, 20 . . . 180 o

8. Also calculate above three terms (step 4, 5, 6) in graphical method (or any analytical method) and

compare with above actual value.

Graph

Angle b/w fixed to crank θ2 vs Velocity ratio of coupler to crank ω3/ω2

Angle b/w fixed to crank θ2 vs Velocity ratio of rocker to crank ω4/ω2

Result:

Thus the angular velocity ratios where calculated and compared with graphical method.

10

TABULATION:

MODEL CALCULATION:

S.No

Angle of

inclination

of driver

(α)

Angle

of

driver

shaft

(θ1)

Angle

turned by

intermediate

shaft

(θ2)

Angle of

driven shaft

(θ3)

dθ1 dθ2 dθ3

Angular

velocity

ratio(exp)

(ω2/ω1)=

dθ2/ dθ1

Angular velocity

ratio(theo)

(ω2/ω1)=

cos α/(1-cos2 θ sin2α)

11

KINEMATICS OF SLIDER CRANK MECHANISM

Exp No:

Date:

Aim: To determine the following to the specification of the crank and connecting rod

1. Angular velocity of connecting rod.

2. Linear velocity of slider and comparing to experiment results with theoretical value by analytical

and graphical method.

Apparatus required:

Experimental setup

Scale

Align key

Formula:

Experimental Method:

ω =10 rad/sec

Linear velocity of slider VP=X ω / θ

Angular velocity of connecting rod ωc = ω ø / θ

Angle between slider & connecting rod Ø=sin-1(sin θ/n)

Theoretical value:

Linear velocity of slider VP= r ω [sin θ +sin2 θ/2n]

Angular velocity of connecting rod ωc = ω cos θ/лcos ø

Theoretical value of displacement x =[ rcos θ + lcos ø]

Where

n= l/r

θ=crank angle

r=radius of crank

Ø=connecting rod angle

l=length of coupler rod

n=ratio of length of coupler rod to radius of crank

Testing procedure:

This model consists of a slider crank mechanism with the following features.

(a) Crank length is adjustable.

(b) Connecting rod length is adjustable.

(c) Crank and connecting rod ends are hinged by ball bearings.

(d) Angular position of crank can be measured to an accuracy of 0.1o

(e) Slider position can be measured to accuracy of 1 mm.

To check it and correct if the correction is needed.

12

Experimental procedure

(1) Set length of crank( r ) and connecting rod ( I ).

(2) Ensure zero reading in crank angle for outer dead centre of crank.

(3) Measure value of position of slider 'x' for various values of crank angle '0', from0, 10, 20 --- 180o

(4) Also calculate above three terms (step 3in graphical method (or any analytical method) and

compare with above actual value.

MODEL CALCULATION:

Graph

Crank angle vs Angle between slider & connecting rod.

Crank angle vs Angular velocity of connecting rod.

Result:

Thus angular velocity is verified and this theoretical value is compared with its practical value.

13

KINEMATICS OF UNIVERSAL JOINTS

Exp No:

Date:

Aim:

To determine the angular velocity ratio for single and double joints.

Apparatus required:

Experimental setup

Formula:

Angular velocity ratio(the)

(ω2/ω1)= cos α/(1-cos2 θ sin2α) Angular velocity ratio(exp)

(ω2/ω1)= dθ2/ dθ1

Where

α = Angle of inclination of driver

θ1= Angle of driver shaft

θ2= Angle turned by intermediate shaft

θ3= Angle of driven shaft

ω2= angular velocity of driver shaft

ω1=angular velocity of driven shaft

Testing procedure:

Check the joints are perfectly

Check the marking scale is correctly or not

Check the initial corrections

Description:

Universal joint (or Hooke's joint) can transmit power between inclined axes. If u is the inclination

between the input and output shaft then, angular velocity of output shaft,

(ω2/ω1)= cos α/(1-cos2θ sin2α)

Where,

ω is the angular velocity of input shaft.

And α is the angle turned by input shaft.

14

It can be seen from the above equation, ω2/ω1 not constant and varies as a function of θ. This will

introduce angular acceleration and hence inertia torque and stresses due to that uniform velocity

ratio (or no angular acceleration) can be achieved by introduction of one more universal coupling in

the same sense to give angular velocity of output shaft, ω2 = ω1 for all values of θ.

Experimental procedure:

The setup consists of two numbers of universal joints joined by a spline shaft. The whole system is

mounted on three Plummer blocks.

Provision is made to measure angular position of input shaft, intermediate shaft and output shaft.

The inclination between shafts can be varied and measured.

MODEL CALCULATION:

15

Result:

Thus the angular velocity ratios where calculated and compared with theoretical values.

16

TABULATION:

MODEL CALCULATION:

Fixed

position

Time taken for 1

revolution

sec

Speed

rpm

Actual ratio of

sun gear

Theoretical ratio

of sun gear

sun annular arm sun annular arm annular arm annular arm

17

EPICYCLIC GEAR TRAIN

Exp No:

Date:

Aim:

To determine the speed for sun, annular and arm and compare with theoretical values.

Apparatus required:

Experimental setup

Stop watch

Formula:

1. Arm fixed:

Speed of the Sun Gear (NS) = 60/ time taken for 1 revolution of sun gear

Speed of the Annular Gear (NA) = 60/ time taken for 1 revolution of annular gear

2. Annular fixed:

Speed of the Sun Gear (NS) = 60/ time taken for 1 revolution of sun gear

Speed of the Arm Gear (Na) = 60/ time taken for 1 revolution of arm gear

3. Actual ratio of sun gear:

Arm fixed:

Annular=NA/NS

Annular fixed:

Arm=Na/NS

4. Theoretical Ratio Of Sun Gear

Arm fixed:

Annular=S/A

Annular fixed:

Arm=1/[(A/S)+1]

Where

S = No of tooth in sun wheel=33

A= No of tooth in annular wheel=63

a= No of tooth in arm wheel=15

Experimental procedure:

Fix the arm by using align screw in arm given power supply to fly wheel through motor and

measure the time taken tor revolution of sun and annular by stopwatch varying revolution in S/A

times of sun wheel.

Fix annular by aligning the screw in annular give power supply to the sun wheel through motor and

measure the time taken for n revolution of sun and annular and verify arm revolution.

Fix the sun and give the hand measure no by revolution by annular axis when there meet in same

position verify the annular revolution in n times of arm revolution.

18

MODEL CALCULATION:

Result:

Thus the sun, annular and arm speed are determined by experimental in epicyclic gear train and

compared with theoretical values.

19

PROELL GOVERNOR

20

TABULATION:

MODEL CALCULATION:

S.No. Voltage

Governor

Speed

N ( rpm )

Deflection

Deflection Radius of

rotation, r

(mm)

Angular

velocity

Controlling force, F

(N) initial scale

21

PROELL GOVERNOR

Exp. No. :

Date :

Aim : To determine the characteristic curves of the Proell Governor.

Apparatus Required:

1. Digital rpm indicator with sensor 3. Sleeve weights

2. Proell arm setup 4. Measuring tape.

Description of the setup:

The drive unit consists of a DC electric motor connected through belt and pulley

arrangement. Motor and test setup are mounted on a M.S. fabricated frame. The governor spindle is

driven by motor through V belt and is supported in a ball bearing.

The optional governor mechanisms can be mounted on spindle. Digital speed is controlled by the

electronic control unit. A rpm indicator with sensor to determine the speed. A graduated scale is

fixed to the sleeve and guided in vertical direction. Sleeve displacement is to be noted on the scale

provided.

The centre sleeve of the Porter and Proell governors incorporates a weight sleeve to which

weights may be added. The Hartnell governor provides means of varying spring rate and initial

compression level and mass of rotating weight. This enables the Hartnell governor to be operated as

a stable or unstable governor.

DC motor with drive: ½ HP motor and DC drive control for speed variation. Separate

linkages for governor arrangements (Porter, Proell and Hartnell) are provided using same motor and

base.

Procedure:

The governor mechanism under test is fitted with the chosen rotating weights and spring,

where applicable, and inserted into the drive unit. The following simple procedure may then be

followed:

The control unit is switched on and the speed control knob is slowly turned to increase

the governor speed until the centre sleeve rises off the lower stop and aligns with some divisions

on the graduated scale. The sleeve position and speed are then recorded. The governor speed is

then increased in steps to give suitable sleeve movements and readings are recorded at each

stage throughout the range of sleeve movement possible. The radius of rotation for

corresponding sleeve displacement is measured directly by switching off the electronic control

unit.

Precautions: 1) Take the sleeve displacement reading when the pointer remains

steady. 2) See that at higher speed the load on the sleeve does not hit the upper sleeve of the

governor. 3) While closing the test bring the pointer to zero position and then switch off the

motor.

22

Formula: Radius of rotation=(a/b)δr

Deflection δ=scale reading –initial reading Controlling Force, F = mω2 r Where,

m = mass of each ball , kgf ω = angular velocity

= ( 2πN ) / 60 (N = speed rpm)

r = radius of rotation

Graphs:

( i ) Governor Speed vs. Radius of rotation

(ii) Governor Speed vs. Controlling force

23

MODEL CALCULATION:

Result:

Thus the characteristic curves of the proell governor are determined.

24

TABULATION:

S.no Speed Angular

Speed Weight

Angle

of

rotation

Time

per 50

deg

rotation

Per

session

(dθ/dt)

Gyroscopic

Torque=

I.ω.ωp

(N.M)

MODEL CALCULATION:

25

MMOOTTOORRIIZZEEDD GGYYRROOSSCCOOPPIICC VVEERRIIFFIICCAATTIIOONN OOFF LLAAWW

Exp No:

Date :

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. Mass moment of Inertia I = mv2/4 kgm3.

2. Angular velocity (ω) =2ЛN/60 rad/sec

3. Angular velocity of precision COP = dθ/dt rad/sec

4. Gyroscopic Couple = I.ω.ωp

Where,

m = mass of the rotor in kg.

R1 = Radius of rotor in cm.

N=spindle speed in rpm

dθ = Angular precision in rad

ω = Angular Velocity in rad

dt = Time required by precision

Procedure:

1. Switch on the supply.

2. Set the require speed of the regulator as constant.

3. Add the load as ½ kg, 1kg etc.

4. Angle of precision dθ i.e. measured.

5. Loose the lock screw, start the stop watch and note down.

6. Watch the particular interval and time.

7. Take the reading n different load.

8. Repeat the equipment maintaining load as constant and varying the speed.

9. Do the calculation.

26

MODEL CALCULATION:

Result:

Thus the Gyroscopic relation was verified.

27

WHIRLING SPEED OF SHAFTS

28

TABULATION:

MODEL CALCULATION:

S.No.

Diameter of

the shaft

material in ‘m’

Speed of

shaft

in ‘rpm’

Vibrating

length

in ‘m’

Natural

frequency of

vibration

Whirling Speed

Theoretical

in rpm

Experimental

in rpm

29

WHIRLING SPEED OF SHAFTS

Exp. No:

Date :

Aim : To determine the whirling speed for various diameter shafts experimentally and

compare it with the theoretical values.

Apparatus Required:

1. Tachometer 3. Steel Rule

2. Vernier Calliper

Description of the setup:

The apparatus is used to study the whirling phenomenon of shafts. This consists

of a frame in which the driving motor and fixing blocks are fixed. A special design is provided

to clear out the effects of bearings of motor spindle from those of testing shafts.

Procedure:

1) The shaft is to be mounted with the end condition as simply supported. 2) The speed of rotation of the shaft is gradually increased.

3) When the shaft vibrates violent in fundamental mode (I mode) , the speed is noted down.

4) The above procedure is repeated for the remaining shafts.

Observation:

Young’s modulus, E (for steel) = 2.06 x 1011

, N / m2

Young’s modulus, E (for copper) = 1.23 x 1011

, N / m2

Length of the shaft, L = , m

Formulae:

Natural frequency, fn = K√¯(gEI/wl4) in Hz

Whirling speed, N = fn x 60 in rpm

Where,

K = 2.45 for fixed and hinged conduction of beam to

first made

g =acceleration due to gravity, 9.81m/s2

w =Weight of the shaft per circuit length in N

l = Length of the shaft, m

E =Young’s modulus for the shaft material, N/m2

I = Mass moment of inertia of the shaft

= (π / 64) d4,

m4

30

MODEL CALCULATION:

Result:

The whirling speed for various diameter shafts are determined experimentally

and verified with the theoretical values.

31

BBAALLAANNCCIINNGG OOFF RROOTTAATTIINNGG MMAASSSS

Exp No:

Date:

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 value of mass and radil.

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

Diagrams:

1 Plane of the masses

2. Angular position of the masses

3. Force polygon

4 Couple polygon

32

TABULATION:

S.No Mass(m)

kg

Radius

(r)

m

Centrifugal

force(m.r)

Kg.m

Distance

from

reference

plane(l)

Couple

(m.r.l)

kgm2

Angle from

reference

plane

MODEL CALCULATION:

Result:

Thus the Balancing Of Rotating Machine Was Verified.

33

DDEETTEERRMMIINNAATTIIOONN OOFF MMOOMMEENNTT OF

IINNEERRTTIIAA OF CONNECTING ROD BBYY

OOSSCCIILLLLAATTIIOONN MMEETTHHOODD

Exp No:

Date:

Aim:

To determine the moment of inertia by oscillation method.

Apparatus Required:

1. Vernier calliper

2. Scale

3. Stopwatch

4. Connecting rod.

Formula Used:

1. Smaller end h = (r1+ (L-x)) in m

2. Bigger end h = (r2 +m) in m

3. K2 exp = (T2exp.g.h)/4Л2h2

4. Texp = t/n in sec

5. Moment of inertia of connecting rod = mk2 in kgm2

Where,

r1 = Smaller end radius

r2 = Bigger end radius

L = length of connecting rod

X = distance of C.G. from small end

M = mass in kg

R = radius of gyration

N = no of oscillations

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.

34

TABULATION:

MODEL CALCULATION

Sl.No. Position

Distance from

OG to

suspension

m

Time for 10

oscillation in sec

Texp

sec

K2exp

m2

Moment of

inertia

time Avg

time Kg-m2

1 Smaller end

2 Bigger end

35

Result:

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

36

TABULATION:

S.No Weight

added m

(kg)

Force

N

Deflection

(mm)

Natural

frequency

fn,

Hz

Stiffness

k (N/m)

MODEL CALCULATION:

37

LONGITUDINAL VIBRATION OF SPRING-MASS SYSTEM

Exp No:

Date:

Aim: To calculate the undamped natural frequency of a spring mass system

Apparatus required:

Weights

Spring setup

Digital indicator

Control panels

Description:

The setup is designed to study the free or forced vibration of a spring mass system either

damped or undamped condition.

It consists of a mild steel flat firmly fixed at one end through a trunnion and in the other

end suspended by a helical spring, the trunnion has got its bearings fixed to a side

member of the frame and allows the pivotal motion of the flat and hence the vertical

motion of a mass which can be mounted at any position along the longitudinal axes of

the flat.

The mass unit is also called the exciter, and its unbalanced mass can create an excitation

force during the study of forced vibration experiment. The experiment consists of two

freely rotating unbalanced discs. The magnitude of the mass of the exciter can be varied

by adding extra weight, which can be screwed at the end of the exciter.

Formula used

Stiffness, k = F/S N/mm

Natural frequency, =1/2Л√g/s in Hz

Where,

G – acceleration due to gravity 9.8 m/s

S – static deflection in mm

F – force in Newton

Procedure:

Determination of spring stiffness

1. Fix the top bracket at the side of the scale and Insert one end of the spring on the

hook.

2. At the bottom of the spring fix the other plat form.

3. Note down the reading corresponding to the plat form.

4. Add the weight and observe the change in deflection.

5. With this determine spring stiffness.

38

MODEL CALCULATION:

Graph:

Load vs Deflection

Load vs stiffness

Result:

Thus the natural frequency of the spring mass system is determined.

39

NATURAL FREQUENCY OF COMPOUND PENDULUM

40

TABULATION:

MODEL CALCULATION:

Sl.No. Length in

‘m’

OG in

‘m’

Time taken for 10

oscillations in

‘sec’

Radius of

gyration, K

Time Period

(sec)

Natural frequency,

Hz

t1

sec

t2

sec

mean

t

sec Kexp Kthe Texp Tthe Fexp Fthe

41

NATURAL FREQUENCY OF COMPOUND PENDULUM

Exp. No. :

Date :

Aim : To determine moment of inertia by using compound pendulum and period and radius of gyration of the given steel bar experimentally and compare it with the theoretical values.

Apparatus Required:

1) Stop Watch

2) Steel Tube

3) Compound Pendulum

4) Supporting Hanger

Description of the setup:

The compound pendulum consists of 100 cm length and 5 mm thick steel bar. The

bar is supported by the knife edge. It is possible to change the length of suspended pendulum

by supporting the bar in different holes.

Procedure:

1) Support the steel bar in any one of the holes.

2) Note the length of suspended pendulum to measure OG.

3) Allow the bar to oscillate and determine Texp by knowing the time taken for n = 10

oscillations.

4) Repeat the experiment with different length of suspension.

Formulae:

1) Theoretical (Kth) = L/√¯3 in ‘m’

2) Experimental (Texp) = t/n in ‘sec’

3) Experimental(Kexp) = [ (Texp/2 π) 2

x g x (OG - OG2) ]½

4) Tth = 2 π [√¯ ( Kexp2

+ ( OG )2

) / ( g (OG)) ] }, sec

5) Fexp = 1/ Texp in Hz

6) Fth = 1/ Tth in Hz

Where,

Kth = Theoretical radius of gyration

42

Kexp = Experimental radius of gyration

OG = distance of the C.G. of bar from support , cm

T exp = Experimental periodic time, in sec

T th = Theoretical periodic time, in sec

MODEL CALCULATION:

43

Result:

Thus the natural frequency of compound pendulum is determined.

44