SCHOOL OF ENGINEERING

ENGINEERING DYNAMICS EM202

LABORATORY MANUAL

Lecturer / Tutor: Ms. Krishnawathy / Ms. Nor Fazilah

Name : ______________________________________

ID : ______________________________________

Course : ______________________________________

FACULTY OF ENGINEERING, ARCHITECTURE & BUILD ENVIRONMENT

UCSI UNIVERSITY

2011

EXPERIMENT 1 – STATIC FRICTION

Objective:

In this lab, you will make some basic measurements of friction. You will measure the coefficients of static friction between several combinations of surfaces using an inclined plane between three of the combinations of surfaces.

This experiment enables the students to determine the static coefficient of friction (µs) between specimens of different materials on different surface using the angle of repose method.

Theory:

The coefficient of static friction s can be measured experimentally for an object placed on an inclined plane (a.k.a. ramp, a.k.a. hill). The coefficient of static friction is related to the critical angle c for the ramp, at which the object just begins to slide. Using what we have covered in class, you can derive this relationship yourself! At this critical angle, static friction preventing the object from sliding down the hill is just exactly equal to the component of the object’s weight along the hill. If the component of the weight along the hill were just a little greater, it would overcome friction, and the object would start to slide down.

Learning Outcome:

Upon completion of experiment, student is able to

1. Measure the static coefficient of friction (µs) between various specimens on different plane surfaces given the mass and normal force.

2. Find the relations between the static coefficient of friction (µs) with repose angle, .

Material and Apparatus:

Inclined Plane Apparatus (LS-12006), specimen (aluminium, steel, brass, wood), plane surface (steel

and plastic), cord, pulley and weight blocks (10g, 20g, 50g, 100g).

Experimental Procedure:

PART I

1. Place the apparatus as shown in Figure 1 on table. Make sure it is levelled.

2. Choose a specimen, identify the material, weigh the specimen (R) and calculate it in recording it into

the table.

3. With plane in the horizontal position, place the specimen somewhere at the mid span.

4. Attach a cord to the specimen and pass the cord over the pulley. Suspend a mass hanger onto the

end the cord.

5. At first, balance the specimen without sliding across the plane by adding load onto the hanger

gradually.

6. Once the specimen is in equilibrium, add weight blocks onto the hanger gradually until the

specimen just starts to move. Record the weight in Newton.

7. Repeat the procedures (2) to (6) three times to compute the average Frictional Force, F and Normal

Force, R.

8. Repeat the procedures (2) to (7) by using specimens of different materials.

9. Repeat step (8) on different surfaces and record your findings.

10. Given, Fs = µsR. Compute the static coefficient of friction, µs.

PART II

11. Repeat steps 1-3.

12. Slowly raise the horizontal plane until the specimen just starts to slide. Note the angle, .

13. Repeat the procedures (7) and (8) by using specimens of different materials.

14. Repeat procedure (13) on different surfaces and record your findings.

15. Given, µs = Tan . Compute the static coefficient of friction, µs.

Results/Finding:

PART I

1. 1.1 Steel surface

Trial Aluminium Steel Brass Wood

R (N) F (N) R (N) F (N) R (N) F (N) R (N) F (N)

1

2

3

Average

µs

1.2 Plastic surface

Trial Aluminium Steel Brass Wood

R (N) F (N) R (N) F (N) R (N) F (N) R (N) F (N)

1

2

3

Average

µs

Figure 1

PART II

2. 2.1 Steel Surface

Trial Aluminum Steel Brass Wood

1

2

3

Average

µs

2.2 Plastic Surface

Trial Aluminum Steel Brass Wood

1

2

3

Average

µs

Discussions:

1. Compare the values of the static coefficient of friction (µs) obtained in two experiments above and

explain.

2. What is the critical tangential force that will cause the surfaces to start to slide?

3. Determine the relation between the static coefficient of friction (µs) and the angle of inclination ().

4. Compare the static coefficient of friction (µs) of different surfaces and explain the differences.

5. Prove that µs = Tan . Include a diagram of all the forces on the specimen as it slides down the

inclined plane.

EXPERIMENT 2 – KINETIC FRICTION

Objective:

In this lab, you will measure the coefficients of kinetic friction between several combinations of surfaces using an inclined plane between three of the combinations of surfaces.

This experiment enables the students to determine the kinetic coefficient of friction (µk) between specimens of different materials on different surface using the angle of repose method.

Theory:

You can calculate the coefficient of kinetic friction, µk, using a variation of the method you used for the coefficient of static friction. For the coefficient of kinetic friction, you can use the same free body diagram but now, the combination of WH and the force of friction will need to add up such that the block will slide at a constant speed. Think of Newton’s first and second laws when you set up this equation.

Learning Outcome:

Upon completion of experiment, student is able to

1. Measure the kinetic coefficient of friction (µk) between various specimens on different plane surfaces given the mass and normal force.

2. Derive a relationship between the critical angle, and the coefficient of kinetic friction (µk). 3. Compare the values of s from Experiment 1 and k from Experiment 2.

Material and Apparatus:

Inclined Plane Apparatus (LS-12006), specimen (aluminium, steel, brass, wood), plane surface (steel

and plastic), cord, pulley and weight blocks (10g, 20g, 50g, 100g).

Experimental Procedure:

PART I

1. Place the apparatus as shown in Figure 2 on table.

2. Choose a specimen, identify the material, weigh the specimen (R) and calculate it in recording it into

the table.

3. With plane in the horizontal position, place the specimen somewhere at the mid span.

4. Attach a cord to the specimen and pass the cord over the pulley. Suspend a mass hanger onto the

end the cord.

5. At first, balance the specimen without sliding across the plane by adding load onto the hanger

gradually.

6. Once the specimen is in equilibrium, add weight blocks onto the hanger gradually until the

specimen moves in a constant speed. *You might have to tap the block to get it moving. Ensure that

the block does not accelerate. Record the weight in Newton.

7. Repeat the procedures (2) to (6) three times to compute the average Frictional Force, F and Normal

Force, R.

8. Repeat the procedures (2) to (7) by using specimens of different materials.

9. Repeat step (8) on different surfaces and record your findings.

10. Given, Fk = µkR. Compute the kinetic coefficient of friction, µk.

PART II

11. Repeat steps 1-3.

12. Slowly raise the horizontal plane until the specimen starts to slide at a constant speed. Note the

angle, .

13. Repeat the procedures (7) and (8) by using specimens of different materials.

14. Repeat procedure (13) on different surfaces and record your findings.

15. Given, µk = Tan . Compute the kinetic coefficient of friction, µk.

Results/Findings:

PART I

1. 1.1 Steel surface

Trial Aluminium Steel Brass Wood

R (N) F (N) R (N) F (N) R (N) F (N) R (N) F (N)

1

2

3

Average

µk

1.2 Plastic surface

Trial Aluminium Steel Brass Wood

R (N) F (N) R (N) F (N) R (N) F (N) R (N) F (N)

1

2

3

Average

µk

Figure 2

PART II –

2. 2.1 Steel Surface

Trial Aluminum Steel Brass Wood

1

2

3

Average

µs

2.2 Plastic Surface

Trial Aluminum Steel Brass Wood

1

2

3

Average

µs

Discussions:

1. Compare the values of the kinetic coefficient of friction (µk) obtained in two experiments above and

explain.

2. Determine the relation between the kinetic coefficient of friction (µk) and the angle of inclination

().

3. Compare the kinetic coefficient of friction (µk) of different surfaces and explain the differences.

4. Does the value of µk dependent on the surface material? Explain.

5. Compare the kinetic coefficient of friction (µk) and static coefficient of friction (µs) obtained from

Experiment 1.

EXPERIMENT 3 – WORK DONE BY VARIABLE FORCES

Objective:

1. To determine the work done by variable effort.

2. To show that work done by effort is equal to the change in potential energy of the load.

Theory:

We have introduced in lecture the concepts of work

and kinetic energy

which are related by the work-kinetic energy theorem

Learning Outcome:

Upon the completion of experiment, student is able to determine the work done by variable effort from

graph and show the relation between work done and change in potential energy of the load.

Material Apparatus:

Work Done by Variable Force Apparatus (LS-12042), 2 pulleys, cord, mass blocks (10g, 20g, 50g, 100g),

long ruler.

Experimental Procedure:

1. Place the apparatus as shown in Figure 3 on a levelled floor.

2. Place the cord onto both of the pulleys.

3. Hang the 100g weight hangers onto the respective hooks on the cord.

4. Measure the initial height of the effort height, he from the floor and record it.

5. Apply additional weights (Fload) by 50g to the load hanger to produce more effort without adding any

additional weight to the effort hanger (Feffort).

6. Measure the height of the effort hanger from the floor, h.

7. Repeat step 5 and 6 by adding more weight on the load hanger.

8. Drafts a table with the data(s) obtained and plot a graph of Fload against displacement for the effort

hanger, H.

9. From the graph, find the area under the graph and this will be the total work done.

Figure 3

Results/Findings:

Effort hanger initial height, hE = ______

Feffort (N) Fload (N) h (mm) H = hE – h

Discussions:

1. Explain the graph obtained in procedure (9).

2. If the amount of work done can be computed using the following equation:

Prove that the amount of work done by the effort load if equals to the change in

gravitational potential energy of the lifted load. Where,

W = mg(hL – hE)

EXPERIMENT 4 – Rolling Disc & Axle

Objective:

To determine the mass moment of inertia of disc using the equation involving the sum of mass and radii

of disc and axle.

Theory:

The moment of inertia I of a body is a measure of how hard it is to get it rotating about some axis. The

moment I is to rotation as mass m is to translation. The larger the I, the more work required to get the

object spinning, just as the larger the mass m, the more work required to get it moving in a straight line.

The moment of inertia is always defined with reference to a particular axis of rotation — often a

symmetry axis, but it can be any axis, even one that is outside the body. The moment of inertia of a

body about a particular axis is defined as:

(1)

where the sum is over all parts of the body (labelled with an index i), mi is the mass of part i, and ri is the

distance from part i to the axis of rotation.

For a disk with an axis through the centre of symmetry, the moment of inertia is

(2)

Learning Outcome:

Upon the completion of experiment, student should be able to compute the value of Moment of Inertia,

I from measuring the masses and radii of disk and axle using equation (1).

Material and Apparatus:

Rolling Disc, Axle, Weighing Scale

Procedure:

1. Use the appropriate measuring tool to measure the diameters to find their radii, r for the

axle and R for the disk. Refer Figure 4 for reference.

2. Take about 3 readings and table them accordingly. Compute the average of your

measurements and estimate the uncertainty in r.

3. Given that the mass of large disc and axle is 2.94kg and mass of small disc and axle is 1.14kg.

Assumptions:

Disc and axle are made of mild steel. Given the density of mild steel is 7860 .

Results/Findings: 1. Length of the axle, laxle = __________

Trials Mass of axle

(kg) maxle

Mass of disc (kg) Mdisc

Radii of disk (mm)

R

Radii of axle (mm)

r 1

2

3

Avg

Discussions:

1. Using Equation (2), find Idisk and Iaxle separately and then compute .

2. Is Iaxle significant, compared to Idisk, or can it be ignored? Discuss.

Figure 4

EXPERIMENT 5 – Rolling Disc On An Inclined Plane

Objective:

To determine the mass moment of inertia of a rolling the disc down an inclined plane using energy

conservation method.

Theory:

Consider the wheel, consisting of disk and axle, rolling down an inclined set of rails after starting from

rest at the top, like so:

The total energy at any time is the sum of the translational kinetic energy, the rotational kinetic energy,

and the gravitational potential energy.

. (3)

Here, M is the total mass of disk + axle, v is its translational speed, ω is its angular velocity, and h is the

height of the centre of mass. Initially, the wheel is at rest at height ho, so its initial kinetic energy (both

translational and rotational) is zero and its total energy is all potential.

Learning Outcome:

Upon the completion of experiment, student should be able to compute moment of inertia, I by timing

the wheel as it rolls down inclined rails and using the principle of conservation of energy.

Material and Apparatus:

Incline plane with adjustable height, 2 stopper blocks, disc with axle, measuring tape, long ruler, and

stop watch.

Procedure:

Diagram 1

Diagram 2

0.7m

H

Figure 5

1. Place the inclined plane apparatus on a level surface and ensure that the top surfaces of the two

rails are levelled. Wipe off any grease and dirt, which may be on the top of the rails.

2. Measure from the table top to the underside of the front rail at each end (a, b) and record the

height in table. Measure the overall length of the rail (Lo) and note the value. Refer Diagram 1.

3. Raise the movable end of the rails to the lowest level so that the rails are almost levelled. Place the

large disc on the rails at the support end and marks its position. *Hold on the disc near the start

block so that once it’s released it should roll freely along the rail.

4. Using the measuring tape, measure about 0.7m along the rail from the centre pivot of the disc axle

and fix the stopper block so that the linear distance travelled by the disc is 0.7m along the rail. Refer

Diagram 2 and Figure 5.

5. Remove the disc and raise end of the rail for about 25mm. Measure the height a and b from the

table top.

6. Place the large disc on the high end of the rails and line up the axle perpendicular to the rails.

Holding it while preparing to use the stopwatch.

7. Measure the time taken for the released disc to roll itself 0.7m down the inclined rails. Repeat this

procedure 3 times and record the average time taken into the table.

8. Raise the support by another 25mm height and repeat the step 5 and 6. And repeat step 7 twice.

9. Repeat the whole experiment for the small disc.

10. Plot the graph of log t against log H for both of the disc on graph paper.

11. Refer to Appendix 1 for the detail calculation.

12. Given that the mass of large disc is 2.94kg and mass of small disc is 1.14kg.

Results/Findings:

Discussions:

1. Starting from equation 1.3 derive equation 1.8. Show the steps clearly.

2. To derive equation 1.8, you need to know the value of r. Draw a simple sketch to define r.

3. Find the moment of inertia, I using equation 1.8.

4. Equation 1.8 in the appendix involves g, the acceleration of gravity. This seems to suggest that you

would get a different value for I if you conducted the same experiment on the moon, where g is

different. But the definition of I does not depend on location. Like the mass m, the moment I of an

object is the same on the moon as on the Earth or anywhere else. So how do you explain the

presence of g in Equation 1.8?

Inclination of rails (mm) Rolling Time (sec)

Feet end, a Support end, b Difference, h Height, H Log H Large disc Small disc

t Log t t Log t

ao bo - - - - - - -

a1 b1

a2 b2

a3 b3

a4 b4

EXPERIMENT 6 – Oscillating Disc

Objective:

To determine the mass moment of inertia of disc specimen using oscillating the disc with added

pendulum.

Theory:

The moment of inertia I of a body is a measure of how hard it is to get it rotating about some axis. The

moment I is to rotation as mass m is to translation. The larger the I, the more work required to get the

object spinning, just as the larger the mass m, the more work required to get it moving in a straight line.

The moment of inertia is always defined with reference to a particular axis of rotation — often a

symmetry axis, but it can be any axis, even one that is outside the body. The moment of inertia of a

body about a particular axis is defined as:

Learning Outcome:

Upon the completion of experiment, student should be able to determine the mass moment of inertia

of disc specimen by using oscillating disc method.

Procedure:

Figure 6

1. Place the knife edge apparatus as shown in Figure 6 on the level table.

2. Screw in the pendulum provided into one side of the disc axle.

3. Place the disc with its axle perpendicular to the knife edge.

4. Using the stopwatch, time a counted number of small amplitude oscillation of the assembly (6 to 10

cycles) for at least five repeats.

5. Record the number of cycles together with the time taken into the table provided.

6. Repeat procedures (1) to (5) with a different mass of the pendulum.

7. Repeat procedures (1) to (6) with the smaller disc.

8. Determine the moment of inertia values by referring to appendix 2 for the detail calculation.

9. Given that the mass of large disc is 2.94kg and mass of small disc is 1.14kg.

Results/Findings:

1. Mass of pendulum: __________________

TRIALS

LARGE DISC SMALL DISC

No of swing Time (sec)

No of swing Time (sec)

t1 t2 tavg t1 t2 tavg

1

2

3

4

5

Average

2. Mass of pendulum: __________________

Mass of large disc, ML =

Mass of small disc, MS =

Radius of axle, r =

Effective length of pendulum, l =

Discussions:

1. Using equation 2.5, calculate the period of oscilation, T for each of the disc.

2. How does the Value of T differ with the mass of the pendulum and size of the disc? Discuss.

3. Calculate the moment of inertia of each disc given the equations in Appendix 3.

4. How does the moment of inertia, I differ with the mass of the pendulum and size of the disc?

Discuss.

TRIALS

LARGE DISC SMALL DISC

No of swing Time (sec)

No of swing Time (sec)

t1 t2 tavg t1 t2 tavg

1

2

3

4

5

Average

Appendix 3

EXPERIMENT 7 – Flywheel

Objective:

1. To verify Newton’s Second Law for rotational motion; = Iα

2. To determine the moment of inertia of a disc and axle from experiment.

3. To determine the frictional torque required to overcome the friction.

Theory:

Frictional torque is the difference between applied torque and observed or net torque and is attributed to resistance to relative motion between surfaces.

τnet = τa + τf Real pulleys have mass and frictional torque. Both result in a lower acceleration for a hanging mass.

First, consider a pulley with mass but no friction. Applying Newton's Second Law to the hanging mass:

ma = mg - T

where m is the mass and a is the acceleration of the

hanging mass and T is the tension in the rope. Rearranging,

T = mg - ma (1) The torque on the pulley is given by:

τ = TR = Iα (2)

were I is the moment of inertia and α is the angular acceleration of the pulley. This can be rewritten as:

I(a/R) = TR

since the tangential acceleration of the pulley is the same as the acceleration of the hanging mass. Rearranging,

T = Ia/R2 [eqn 2] Combining equations 1 and 2:

mg - ma = Ia/R2

So acceleration can be calculated from

Learning Outcome:

Upon the completion of experiment, student should be able to determine the moment of

inertia of a disc and axle from experiment and the frictional torque required to overcome the

friction.

Procedure:

1. Measure the diameter of disc and axle; thickness of disc and length of axle using proper measuring

instruments.

2. Wind the string securely at a comfortable distance from the centre of the disc; around the axle six

turns and make sure the string hangs freely. Record this distance as r.

3. Suspend a mass block, m of 50g on the loose end of the string and support the mass with your

hands to avoid it from spinning loose. Refer Figure 7.

4. The same person holding the mass block should also be taking the time. Release the mass from rest

takes the time taken for the mass to fall free from the axle (6 turns).

5. Without stopping the stop watch, record the time taken for the disc to come to rest after the mass

block has fallen off the axle.

6. Repeat procedures (2) to (5) about 3 times and get the average reading. Record the results into a

table.

Figure 7

7. Repeat procedures (2) to (5) for masses of weight 60g, 70g and 80g.

8. Use the equation α = 24π/t2 to determine the angular acceleration corresponding to each value of

masses, m, used. Use the equation a = rα to determine the linear acceleration for each value of m

and use the equation = mr (g-a) to determine the torque applied to the disc and axle for each

value of m. Tabulate all the values calculated above.

9. Plot a graph of torque, against corresponding values of angular acceleration, α and determine the

slope of a best straight line representing the plotted points.

10. Extrapolate the best straight line of the graph to intersect the torque axis. The point of intersection

should correspond to the positive torque and zero angular acceleration. This non-zero torque can

be interpreted as the torque required to overcome the friction. Determine the frictional torque

from the graph.

11. Calculate the total moment of inertia of the disc and the axle given the density of the disc and axle

is 7860kg/m3. Use M= 휌휋푟 푙 to find mass of the disc and axle respectively.

12. In step 5 of the procedure it was the frictional torque that caused the disc to slow down and finally

to stop. Use the equation = Iα to determine the frictional torque. Use the value of I calculated

from step 9. The angular deceleration, α, can be determined by first calculating the angular velocity

at the instant the string fell off the axle using ωf = 2ωAV and ωi = 12α/t. Then use α = Δω/t to

determine the angular deceleration. Compare the frictional torque found here to that found in

step 10.

Results/Findings:

2. Diameter of the disc, D = __________

3. Diameter of the axle, d = __________

4. Depth of the disc, ldisc = __________

5. Length of the axle, laxle = __________

6. Record all the data(s) collected above in a table. Ensure the data(s) are well tabled.

Discussions:

1. Draw a force diagram to indicate all forces acting on the fly wheel and hanging mass. State clearly

all assumptions made and define any symbols and/or parameters used in the drawing.

2. Using the diagram above, derive equation

3. How do the two values of frictional force obtained above differ? Explain.

= mr (g-a)

EXPERIMENT 8 – Hooke’s Law & Simple Harmonic Motion

Objective:

1. To investigate Hooke’s Law (the relation between force and stretch for a spring)

2. To investigate Newton's Laws and the operation of a spring scale.

3. To compute the spring coefficient, k for an individual spring using both Hooke’s Law and the

properties of an oscillating spring system.

4. It is also possible to study the effects, if any, that amplitude has on the period of a body

experiencing simple harmonic motion.

Theory:

PART I

If an applied force varies linearly with position, the force can be defined as F=kx where k is called the

force constant. Once such physical system where this force exists is with common helical spring acting

on a body. If the spring is stretched or compressed a small distance from its equilibrium position, the

spring will exert a force on the body given by Hooke's Law, namely

Fs=-kx

where is known as the spring force. Here the constant of proportionality, , is known as the spring

constant, and is the displacement of the body from its equilibrium position (at = 0 ). The spring

constant is an indication of the spring's stiffness. A large value for indicates that the spring is stiff. A

low value for means the spring is soft. Generally speaking, springs with large values can balance

larger forces than springs with low values.

Figure 1a.When the displacement is to the right ( > 0) the spring force is directed to the left ( < 0).

Figure 1b.When the displacement is to the left ( < 0) the spring force is directed to the right ( > 0).

Figure 1c. In both cases shown in Figures 1a and 1b, the effect of the spring force is to return the system to the equilibrium position. At this position, = 0 and the spring is unstretched, signifying = 0.

The negative sign in Equation 1 indicates that the direction of is always opposite the direction of the

displacement. This implies that the spring force is a restoring force. In other words, the spring force

always acts to restore, or return, the body to the equilibrium position regardless of the direction of the

displacement, as shown in Figures 1a - 1c.

When a mass, , is suspended from a spring and the system is allowed to reach equilibrium, as shown

in Figure 2, Newton's Second Law tells us that the magnitude of the spring force equals the weight of

the body, . Therefore, if we know the mass of a body at equilibrium, we can determine the

spring force acting on the body.

Figure 2. A body of mass, , is suspended from a spring having a spring constant, . If the system is in equilibrium the spring force is balanced by the weight of the body.

Equation 1 applies to springs that are initially unstretched. When the body undergoes an arbitrary

displacement from some initial position, , to some final position, , this equation can be written as

Where is the body's displacement.

PART II

If the body in Figure 4 is displaced from its equilibrium position some maximum distance, , and then

released, it will oscillate about the equilibrium position. The body will move back and forth between the

positions and . When the mass travels from the maximum displacement to the

minimum displacement and then back to the position , we say that the mass has moved

through one cycle, or oscillation. When an oscillating mass (as in the case of a mass bouncing on a

spring) experiences a force that is linearly proportional to its displacement but in the opposite direction,

the resulting motion is known as simple harmonic motion. This motion is periodic, meaning the

displacement, velocity and acceleration all vary sinusoidally. The time required for the body to complete

one oscillation is defined as the period, , and is given by

Notice the period is dependent only upon the mass of the oscillating body and the spring constant, .

As the stiffness of the spring increases (that is, as increases), the period decreases which has the

effect of increasing the body's average velocity. Conversely, an increase in the body's mass means the

period will also increase, thereby requiring more time for the body to move through one oscillation. It

should be noted that the period of motion is independent of the amplitude of the oscillations.

Learning Outcome

Upon completion of the experiment, student should be able to illustrate and verify the principles and

relations involved in the study of vibrations. And at the same time, determine the spring coefficient ,

for an individual spring using both Hooke's Law and the properties of an oscillating spring system at

single degree freedom and compare the theoretical and experimental natural frequency.

Procedure:

PART I

Figure 8

1. Assemble the apparatus as shown in Figure 8. Hang the extension hook to the lower end of the

spring.

2. Take the initial reading of the pointer on the extension scale. Slowly place the hanger and weight

on the extension hook. Record new position of the pointer after the mass is added.

3. From this, you will calculate the force applied to the spring and the resulting stretch of the spring.

You should allow for at least 5-6 trials with different mass blocks added to it each time. Perform the

experiment systematically by adding the lighter mass first followed by the heavier ones.

4. For each trial, record the mass, the starting position of the spring (before hanging the mass) and

the ending position of the spring (while it is being stretched).

5. Tabulate the data obtained above and plot a graph, Force (Newton) versus Stretch @ Displacement

(mm).

PART II

6. Assemble the apparatus as shown in the diagram above. Hang the extension hook to the lower end

of the spring.

7. Suspend the spring and record its position from the end of the spring without any load added to it.

Refer diagram to the right.

8. After that add a weight about 10g onto the hook and stretch the spring about 30cm and record the

time taken for the spring to come to rest. Also record the number of oscillations made by the

spring.

9. Remove the weight and repeat procedure 9 with heavier weights e.g., 30g and 50g.

10. Tabulate the data collected.

RESULTS/FINDINGS

Tabulate your data obtained from Part I and Part II.

1. Plot a graph of Force (N) vs. displacement (m).

DISCUSSIONS

1. How your graph does looks like?

2. Do your results confirm or contradict Hooke's Law? Please elaborate.

3. Calculate coefficient of spring, k from the graph.

4. In Part II, how does the mass affect the oscillation of spring?

5. From the formula given, compute the spring coefficient, k.

6. How does the value of k obtained from both experiments above differ? Explain why?

EXPERIMENT 9 – Free and Damped Vibration

Objective:

5. To show the discomfort and dangers that result from the resonance phenomenon.

6. To study the effect of adding an absorber to a vibratory resonant system.

7. To compute the damping ratio of a vibrating system.

Theory:

Forced vibration is the one in which external energy is added to the vibrating system. The amplitude of a

forced-undamped vibration would increase over time until the mechanism was destroyed. The

amplitude of a forced-damped vibration will settle to some value where the energy loss per cycle is

exactly balanced by the energy gained.

Examples of this type of vibration include a structure subjected to vibrating machines, vibration of a

building during an earthquake or under the action of wind, etc.

Learning Outcome

Upon completion of the experiment, student should be able to illustrate and verify the principles and

relations involved in the study of vibrations. And at the same time, determine the spring coefficient of

spring at single degree freedom and compare the theoretical and experimental natural frequency.

Procedure:

Figure 9

1. Place the apparatus on a level table as shown in Figure 9.

2. Setup the free and damped apparatus by choosing the desired spring.

3. Adjust the height of the motorized chart recorder, so that it can record the vibration of the spring

accurately and clearly.

4. To measure the un-damped vibration of the spring, remove the nut from the air damper.

5. Oscillate the spring.

6. Slightly turn the graph and place 5N mass block onto it.

7. Repeat step 5 and step 6 for mass blocks of size 10N, 15N, 20N and 25N.

8. Discuss the finding from the graph paper.

9. Place back the nut from air damper to measure damped vibration of the spring. Repeat step 5, 6, 7

and 8.

10. Given the RPM of the motorized chart recorder is 5rpm, diameter of drum is 34.39mm and

circumference of it is 108.05338mm.

Results/Findings:

Discussions:

1. Referring to the equations given in Appendix, calculate the natural frequency of the spring.

2. Find the damping ratio, 휀 = 1− .

Appendix