UNIVERSITI TEKNOLOGI MARAFAKULTI KEJURUTERAAN KIMIAENGINEERING PHYSICS LABORATORY(CHE175)NAME : ABDUL HALIM BIN NORDIN MUHAMMAD RAZI BIN ZAHARI SITI NOR SAMRAH BIN A.RAHIM NOOR SYAFIQAH AMERAH AHMAD TARMIZI NURUL ADILAH BT NASARUDDIN

STUDENT NO. : 2008293172 2008424824 2008291992 2008293072 2008292022

EXPERIMENT : SIMPLE HARMONIC MOTION: MASS ON SPRINGDATE PERFORMED : 4 FEBRUARY 2009

GROUP : 2

PROGRAMME /CODE : DIPLOMA OF CHEMICAL ENGINEERING/EH 110

NOTITLEALLOCATED MARK (%)MARKS (%)

1Abstract/Summary5

2Introduction5

3Objectives5

4Theory5

5Procedure3

6Apparatus5

7Result20

8Calculations10

9Discussions20

10Conclusions10

11Recommendations5

12References5

13Appendices2

Total100

Remarks :Checked by : Recheck by: SUMMARYThis experiment is about simple harmonic motion. Simple harmonic motion refer to the oscillation of an object about its equilibrium position with its acceleration being directed towards the equilibrium position and directly proportional to the displacement from the equilibrium position. This experiment is divided by 2 categories which are 3A (mass on a spring) and 3B: oscillations and waves.

In experiment 3A, different value of mass was used to determine the period calculated. The value of k was constant. All the number of oscillations for all the masses was 5. Period of each oscillations were calculated and the average value was gained.

For experiment 3B, 6 set of length in meter, are used. Count until 20 oscillations. The time for 20 oscillations was obtained by the timer. There are 2 trial were done to get the average time. The time for a single oscillation is calculated.

INTRODUCTIONSimple harmonic motion refer to the oscillation of an object about its equilibrium position with its acceleration being directed towards the equilibrium position and directly proportional to the displacement from the equilibrium position. Simple harmonic motion (SHM) is the back and forth motion of objects around a point. Swings, trees swaying in the breeze, pendula, a boat bobbing on the ocean, and the swinging of your relaxed arm as you walk are all examples of SHM. For SHM to occur there must be a force that pushes the object back to a preferred (equilibrium) position. When that force is proportional to the distance away from equilibrium, then SHM can happen. Mathematically we write this as F = -kxwhere k is a constant and x is the distance away from the equilibrium position. The minus sign indicates that the force is always pointing towards 0. When the mass is to the right of 0, the force is to the left, and vice versa.

Figure 1 illustrates a mass at one instant during its back and forth motion between A and -A.

The points x = A are the biggest distances away from 0. A is called the amplitude. The back and forth motion is also called oscillation of the mass. A mass on the end of a spring is an excellent example of a system that will exhibit SHM. Newton's second law, Fnet = ma, applies to a mass hanging from a spring. If we hang a mass from a spring and let it come to rest, then two forces are acting but there is no acceleration Fnet = mg - kx = 0, and the added weight will equal the spring constant times the distance the spring moved. This relationship is used for the first experiment. When we pull the spring away from equilibrium and let it go, then the only force (away from equilibrium) is the restoring force Fnet = -kx and this will equal ma. This is used for the second experiment, when the motion repeats itself. The time for one repeat cycle is called the period. If we call the period of the motion T, it can be shown that. kmT2 A mass oscillating on a spring is a very interesting example of energy conservation. For some of the time the mass is moving fast, and other times the mass is stopped. Thus, kinetic energy is converted into potential energy and then back to kinetic, over and over, right before your eyes.

OBJECTIVESExperiment 1 Objective of this experiment is to determine whether the vertical motion of a mass dangling from a spring is a good approximation to SHM by two sets one measurement. We also measure the distance the spring stretches when different weights are added to see if F = - kx. If it does, then you will determine. We can measure the period of the motion for several different masses attached to the spring to see if the period varies in accord with the resultT = 2 m/k, for SHM.

Experiment 2

Objective of this experiment is to determining the acceleration due to gravity, g using a simple pendulum.

THEORY

Experiment 1

Figure above shows a mass hanging from a spring. At rest, the mass hangs in a position such that the spring force just balances the gravitational force on the mass. When the mass is below this point, the spring pulls it back up. When the mass is above this point, gravity pulls it back down. The net force on the mass is therefore a restoring force, because it always acts to accelerate the mass back toward its equilibrium position.In the experiment 1 you investigated Hooke`s Law, which states that the force exerted by a spring is proportional to the distance beyond its normal length to which it is stretched (this also holds true for the compression of a spring). This idea is stated more succinctly in the mathematical relationship: F = -kx; where F is the force exerted by the spring fro its equilibrium position and k is the constant of proportional called the spring constant.

Whenever an object is acted on by a restoring force that is proportional to the displacement of the object fro its equilibrium position the resulting motion is called Simple Harmonic Motion. When the simple harmonic motion of a mass (M) on a spring is analyzed mathematically using Newton`s Second Law (the analysis requires calculus, so it will not be shown here), the period of the motion (T) is found to be:

T = 2Experiment 2

A simple pendulum may be described ideally as a point mass suspended by a massless string from some point about which it is allowed to swing back and forth in a place. A simple pendulum is made up of a plum bob hung from a non extensible string whose mass can be ignored. When the plum bob is displaced to one side from its equilibrium position and then released, it will oscillate around the equilibrium position and a periodic motion is produced. Is this motion simple harmonic nature?

A condition for simple harmonic motion is that the restoring force is proportional to the displacement, x, from the equilibrium and in the opposite direction of the displacement. In the case of the pendulum, the path of the plum bob is not linear but a curve of a circle of radius L, where L id the length of the pendulum. The displacement, x, in this case refers to the distance along this curve measured from the equilibrium point, 0.F = -kx is the formula for a simple harmonic motion, where k is constant, but x = L, where is the angular displacement of the string in radians (360 = 2 radians). If the mass of the plumb bob is, the restoring force will be F = -mg sin . The restoring force is not proportional to but proportional to sin . Therefore the motion of the pendulum bob is not simple harmonic.

But if is small such that sin is approximately , the equation then becomes F = -mg = -mg x/L or F = - (mg/L)x

This shows that the restoring force is proportional to the displacement, x, for small angular displacement, . The constant mg/L represents the force constant, k, in the Simple Harmonic Motion formula.

The period of oscillation for small amplitude oscillations is give by

ORT=4L/g

where g is the acceleration due to gravity. Thus if T2 is plotted against L the slope of the straight line will be 4 2/ g

APPARATUS EXPERIMENT 1 Experiment board Spring balance Mass hanger Masses Stopwatch EXPERIMENT 2 A plum bob Stopwatch Non-extensible string retort stand Meter stick clamps wooden blocks

PROCEDURESEXPERIMENT 1Measuring the value of the constant force, k.1. The hanger without the load was measured.2. 125g mass (total mass of hanger and load) was hanging up to the spring. The displacement of the spring was measured and put it in the table.3. Procedure one was repeated with another value (175g and 225g).4. A graph Force versus Displacement is plotted.5. From the graph, the k of the spring has being measured.

Measuring the period.

1. The equipment is set up as shown in the figure 10.1, with the total mass is 125g. The Spring Balance surely must be vertical so the rods hang straight down through the hole in the bottom of the balance to minimize the friction against the side as the mass oscillates.2. The rod is pulled down for a few centimeters. The rod then being let go up and down after the mass is steady. This step was repeated to make sure it can be released smoothly without friction..3. The mass oscillating was set. The times for as many oscillations can be conveniently counted is measured. The mass, the time and the number of oscillations counted was recorded in the table. The total time is divide by the number of oscillation observed to measure the period of the oscillations. Then it had been recorded in the table.4. The measurement was repeated for five times and the period for each measurement was calculated. Then the average period is measured and was put in the table.5. The equation given at the beginning of this experiment was used to find the period. This value then was put in the table.6. Process 1-5 is repeated with the mass 175g and 225g.

EXPERIMENT 21. The experiment was set as showed in figure 11.1. The mass was swung as the angle was keep reasonably small. The time it takes for at least 30 full oscillations was measured. In table 11.1, the mass, the distance L, the time, and the number of oscillations counted was recorded.

2. The period of the oscillation can be determined by dividing the total time by the number of oscillations observed.

3. The measurement was repeated 5 times. The period for each measurement was calculated.

4. The average period was determined by add the five period measurement together and divide it by five.

5. Then the measurement was repeated by using different length.

6. Theoretical value have to calculate and entered in the table.

RESULT

Mass (kg)# OscillationTimes(s) (measured)Period(s) (average)Period(s) (calculated)

0.125

103.003.003.003.00 3.00

1.55

=0.3

0.360

0.175

104.004.004.004.004.00

2.05

=0.40

O.426

0.225

105.005.005.005.005.00

2.55

=0.50

0.483

EXPERIMENT 1

EXPERIMENT 2Mass (kg)L (m)oscillationsTime (s)(measured)Period (s)(average)Period (s)(calculated)

0.10

0.133026.026.026.026.026.0 4.335 =0.87

226.3

0.173029.029.029.029.029.04.835 =0.97

173.1

0.213031.031.031.031.031.05.175 =1.03

140.1

SAMPLE OF CALCULATION.EXPERIMENT 1The method to calculate the average period (S)

* The formula to calculate the period (T):

T = Time (S) # Oscillations

For using 0.125kg of mass

Measurement 1: T = 3.00 s 10 = 0.300 s

Measurement 2: T = 3.00 s 10 = 0.300s

Measurement 3: T = 3.00 s 10 = 0.600 s

Measurement 4: T = 3.00 s 10 = 0.600 s

Measurement 5: T = 3.00 s 10 = 0.300s

Then, add this five period measurement together and divided by five to determine the average period : * Average period (S) = Total Period (S) 5= (0.300 x 5) S5 = 0.300s

For using 0.175 kg of mass

Measurement 1: T = 4.00 s 10 = 0.400 s

Measurement 2: T = 4.00 s 10 = 0.400 s

Measurement 3: T = 4.00 s 10 = 0.400 s

Measurement 4: T = 4.00 s 10 = 0.400 s

Measurement 5: T = 4.00 s 10 = 0.400 s

Then, add this five period measurement together and divided by five to determine the average period : * Average period (S) = Total Period (S)5= (0.400 X 5) S5 = 0.400 s

For using 0.225 kg of mass

Measurement 1: T = 5.00 s 10 = 0.500 s

Measurement 2: T = 5.00 s 10 = 0.500 s

Measurement 3: T = 5.00 s 10 = 0.500 s

Measurement 4: T = 5.00 s 10 = 0.500 s

Measurement 5: T = 5.00 s 10 = 0.500 s

Then, add this five period measurement together and divided by five to determine the average period : * Average period (S) = Total Period (S)5= (0.500 X 5 ) S5 = 0.500 s

SAMPLE OF CALCULATION.

1) Measure k, the spring constant for the spring in the Spring Balance. From the graph, we can calculate the value of the spring constant, k. With use the formula to calculate the slope of the straight line, so we also can obtain the spring constant.

The formula to calculate the period of the motion (T)s is :

T = 2M(kg) k k=38.0

For using 0.125kg of mass

T = 2 0.125kg 38.0 = 0.360 sFor using 0,175kg of mass

T = 2 0.175kg 38.0 = 0.426 s

For using 0.225kg of mass

T = 2 0.225kg 38.0 = 0.483 s

2) Does your theoretical value for the period accurately predict your experiment value? Yes, the theoretical value for the period is accurately predicting this experiment value.

3) Does the equation for the period of an oscillation mass provide a good mathematical model for the physical reality? Yes, the equation for the period of an oscillation mass is provided a good mathematical model for the physical reality

EXPERIMENT 2

The method to calculate the average time for 30 oscillation, t (sec).

1) To calculate the average time for 30 oscillations, t (sec):

Average time for 30 oscillation, t (sec) = Total time for 30 oscillation, t (sec) 52) Then, divide this average by 30 to determine the average time for a single oscillation, T (sec).

Average time for a single oscillation,

T (sec) =Average time for 30 oscillation, t (sec) 30

For using 0.13 L (m)Measurement 1: T = 26.00 s 30 = 0.867 sMeasurement 2: T = 26.00 s 30 = 0.867 s

Measurement 3: T = 26.00 s 30 = 0.867 sMeasurement 4: T = 26.00 s 30 = 0.867 sMeasurement 5: T = 26.00 s 30 = 0.867 s

Then, add this five period measurement together and divided by five to determine the average period : * Average period (S) = Total Period (S)5= ( 0.867 x 5) S5 = 0.867 s

For using 0.17 L (m)Measurement 1: T = 29.00s 30 = 0.967sMeasurement 2: T = 29.00s 30 = 0.967s

Measurement 3: T = 29.00s 30 = 0.967s

Measurement 4: T = 29.00s 30 = 0.967s

Measurement 5: T = 29.00s 30 = 0.967s

Then, add this five period measurement together and divided by five to determine the average period : * Average period (S) = Total Period (S)5= ( 0.967 x 5) S5 = 0.967s

For using 0.21 L (m)Measurement 1: T = 31.00 s 30 = 1.03 sMeasurement 2: T = 31.00 s 30 = 1.03 s

Measurement 3: T = 31.00 s 30 = 1.03 s

Measurement 4: T = 31.00 s 30 = 1.03 s

Measurement 5: T = 31.00 s 30 = 1.03 s

Then, add this five period measurement together and divided by five to determine the average period : * Average period (S) = Total Period (S)5= ( 1.03 x 5) S5 = 1.03 s

EQUATION

x = L

F = mg x L

For using 0.13mx = (0.13m) (30) = 3.9F= ((0.100kg)(9.8N/m))/((0.13m)) (3.9) = 29.4 N

For using 0.17mx = (0.17 m) (30) = 5.1F= (5.1) = 29.4 N

For using 0.21mx= (0.21m) (30) = 6.3F= (6.3) = 29.4 N

2) Does the period of the oscillations depend on the mass of pendulum? Yes, the larger the mass, the higher period of the oscillations value will achieved. 3) Does your theoretical value for the period accurately predict your experiment value? Yes, the theoretical value for the period is accurately predicting this experiment value.4) Does the equation for the period of an oscillation mass provide a good mathematical model for the physical reality? Yes, the equation for the period of an oscillation mass is provided a good mathematical model for the physical reality

Data analysis

1. Plot a graph of T vs L2. Draw a straight line passing through the data points.3. Obtain the slop of the straight line from the graph, and then the acceleration due to gravity, g, from the slop.4. Slop of the straight line from the graph, m = 4 / g. therefore g = 4 / m

Length of pendulum, L(m)T

0.13T=4L/g =4 0.13 m /9.81m/s =4.54 s

0.17T=4L/g =40.17m /9.81m/ s =5.19 s

0.21T=4L/g =40.21m /9.81m/ s =5.78 s

Data analysis for experiment 2:

M = ( y1 - y2 ) ( x1 - x2 )

= (5.78- 4.54 ) s (0.21 - 0.13) m = 15.5 s2/m

The gravity from the graph usingM = 4 2 gg = 4 2 m = 4 2 15.5 s/m = 2.55 ms-2

(Gradient of graph = 4 2 / g ) g = 4 2 / m = 4 2 / (T2 / L) = 4 2 L / T2 = (M) / (S2) = ms-2

Percentage difference = (9.81 -2.55) x 100% 9.81 = 74.01%

DISCUSSIONEXPERIMENT 1

In experiment 1, we varied the mass which were; 0.125 kg, 0.175 kg, 0.225 kg. The oscillations for all the mass were constants which was 10. For 0.125 kg, the time in second measured for all the oscillations were 3 second. Next, we change the mass to 0.175 kg and the time measured for the oscillations were 4 seconds. Last, for the mass of 0.225 kg, the time measured were 5 seconds. The average period was gained by plus all the time measured and divides by 5 oscillations. The period was calculated using the formula T = 2M (kg)/k and the value were 0.360 s for 0.125 kg, 0.426 s for 0.175 kg, 0.483 s for 0.225 kg respectively. The mass is directly proportional to the period.

EXPERIMENT 2

For experiment 2, the length of the pendulum was change from 0.13 m, 0.17 m and 0.21 m.The time was measured twice so that the average time was gained. To get the time for a single oscillations, the average time was divided by 30 for 30 oscillations. From the data, we can plot the graph of T versus the length of the pendulum. From the graph, we can determine the slope of the graph which was 15.5 s/m. using the slope, we can calculate the value for the gravity. From the graph, we can conclude that the length of pendulum is directly proportional to T.

CONCLUSIONS

In experiment 1, we can conclude that the motion of a simple pendulum is verified to be a simple harmonic motion as it is consistent with the properties of simple harmonic motion. When the mass was changed, the value of the period calculated also change. The larger the mass, the higher period value will achieved.

For experiment 2, graph T vs. length of the pendulum, L was plotted. . The percent difference for the theoretical value of gravity and the value of calculated gravity was 74.01%. From the graph, we can conclude that when you change the length of the pendulum, the period of the pendulum does change. The shorter the string, the shorter the period.

There are some errors that affected the results of the experiment, such as errors caused by friction exerted on the paper tape attached to the pendulum mass, air resistance and the error caused by the inaccuracy of the ticker-timer.

RECOMMENDATION1. The air resistance is neglecting, so make sure that the fans are closed.

2. Try to hang pendulum plumb not so closed to wall, as they will collapse with each other, this will change the value or data`s obtained because the oscillation between The wall and the wall and the pendulum plumb. 3. Make sure the timer take the time accurately.

REFERENCES PHYSIC GIANCOLI (SIXTH EDITION) DOUGLAS C. GIANCOLI

MANUAL LAB ENGENEERING PYHSICS LABAROTORY (CHE 175)

PROGRAM MATRIKULASI MODUL FIZIK EDISI PERTAMA 1999 PROF. MADYA DR. ELIAS SAION PROF MADYA DR. AZIZAN ISMAIL

APPENDICES