THE SIMPLE PENDULUM
ITS PERIOD OF OSCILLATION
TO MEASURE G= 9.807 MS-2
AND AS A CLOCK

NAME:

CLASS:

TEACHER:

EXAMINATION CODE:

NRIC NO. :

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Contents

1. INTRODUCTION
 PENDULUM
 HISTORY OF PENDULUM

 MAIN BODY
 EXPERIMENTAL PROCEDURE
 GRAPH OF T AGAINST L
 PLOTTING OF TWO DIFFERENT VARIABLES
 COUNTING OF GRAVITATIONAL ACCELERATION
 SIMPLE PENDULUM AS A DEVICE
 TO MEASURE TIME

2. FURTHER EXPLORATION

3. CONCLUSION

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Introduction

Pendulum

A pendulum is a mass that is attached to a pivot, from which it can swing freely. This object is subject to a restoring force due to gravity that will accelerate it toward an equilibrium position. When the pendulum is displaced from its place of rest, the restoring force will cause the pendulum to oscillate about the equilibrium position.
A basic example is the simple gravity pendulum or bob pendulum. This is a mass (or bob) on the end of a massless string, which, when initially displaced, will swing back and forth under the influence of gravity over its central (lowest) point.
The regular motion of the pendulum can be used for time keeping, and pendulums are used to regulate pendulum clocks.
History of Pendulum
As recorded in the 5th century Chinese Book of Later Han, one of the earliest uses of the pendulum was in the seismometer device of the Han Dynasty (202 BC - 220 AD) scientist and inventor Zhang Heng (78-139). Its function was to sway and activate a series of levers after being disturbed by the tremor of an earthquake far away. After this was triggered, a small ball would fall out of the urn-shaped device into a metal toad's mouth below, signifying the cardinal direction of where the earthquake was located (and where government aid and assistance should be swiftly sent). An Egyptian scholar, Ibn Yunus, is known to have described an early pendulum in the 10th century.

Galileo Galilei
Among his scientific studies, Galileo Galilei performed a number of observations of all the properties of pendulums. His interest in the pendulum may have been sparked by looking at the swinging motion of a chandelier in the Pisa cathedral. He began serious studies of the pendulum around 1602. Galileo discovered the key property that makes pendulums useful timekeepers: isochronism, which means that the period of the pendulum is approximately independent of the amplitude (width) of its swing, so that successive swings of the pendulum will take the same amount of time even if the swing is decreasing due to friction. He also found that the period of a pendulum is independent of the mass of its bob, and proportional to the square root of its length. The isochronism of the pendulum suggested a practical application for use as a metronome to aid musical students, and possibly for use in a clock.
Perhaps based upon the ideas of Galileo, in 1656 the Dutch scientist Christiaan Huygens patented a mechanical clock that employed a pendulum to regulate the movement. This approach proved much more accurate than previous time pieces, such as the hourglass. Following an illness, in 1665 Huygens made a curious observation about pendulum clocks. Two such clocks had been placed on his fireplace mantel, and he noted that they had acquired an opposing motion. That is, they were beating in unison but in the opposite direction—an anti-phase motion. Regardless of how the two clocks were adjusted, he found that they would eventually return to this state, thus making the first recorded observation of a coupled oscillator.
During his Académie des Sciences expedition to Cayenne, French Guiana in 1671, Jean Richer demonstrated that the periodicity of a pendulum was slower at Cayenne than at Paris. From this he deduced that the force of gravity was lower at Cayenne. Huygens reasoned that the centripetal force of the Earth's rotation modified the weight of the pendulum bob based on the latitude of the observer.
In his 1673 work Horologium Oscillatorium sive de motu pendulorum, Christiaan Huygens published his theory of the pendulum. He demonstrated that for an object to descend a curve under gravity in the same time interval, regardless of the starting point, it must follow a cycloid curve, rather than the circular arc that a pendulum follows. This confirmed the earlier observation by Marin Mersenne that the period of a pendulum does vary with amplitude, and that Galileo's observation of isochronism was accurate only for small swings in the neighborhood of the center line.
The English scientist Robert Hooke devised the conical pendulum, consisting of a pendulum that is free to swing in both directions. By analyzing the circular movements of the pendulum bob, he used it to analyze the orbital motions of the planets. Hooke would suggest to Isaac Newton in 1679 that the components of orbital motion consisted of inertial motion along a tangent direction plus an attractive motion in the radial direction. Isaac Newton was able to translate this idea into a mathematical form that described the movements of the planets with a central force that obeyed an inverse square law—Newton's law of universal gravitation. Robert Hooke was also responsible for suggesting (as early as 1666) that the pendulum could be used to measure the force of gravity.
In 1851, Jean-Bernard-Leon Foucault suspended a pendulum (later named the Foucault pendulum) from the dome of the Panthéon in Paris. It was the third Foucault pendulum he constructed, the first one was constructed in his basement and the second one was a demonstration model with a length of 11 meters. The mass of the pendulum in Pantheon was 28 kg and the length of the arm was 67 m. The Foucault pendulum was a worldwide sensation: it was the first demonstration of the Earth's rotation with a purely indoors experiment. Once the Paris pendulum was set in motion the plane of motion was observed to precess about 270° clockwise per day. A pendulum located at either of the poles will precess 360° per day relative to the ground it is suspended above. There is a mathematical relation between the latitude where a Foucault pendulum is deployed and its rate of precession; the period of the precession is inversely proportional to the sine of the latitude.
For 270 years, from their invention until quartz crystal oscillators superseded them in the 1920s, pendulums were the world's most accurate timekeeping technology. The most accurate pendulum clocks, called astronomical regulators, were installed in astronomical observatories, and served as standards to set all other clocks. The National Institute of Standards and Technology based the U.S. national time standard on the Riefler clock made by the German firm Clemens Riefler, from 1904 until 1929. This pendulum clock maintained an accuracy of a few hundredths of a second per day. It was briefly replaced by the double-pendulum W. H. Shortt clock, before the NIST switched to quartz clocks in the 1930s.

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Procedure

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Conclusion

My data showed the period of my simple pendulum to be independent of mass, which is consistent with the uncertainty of the measurements made with the stopwatch.

Time is measured to the nearest 0.01s but I might expect the vagueness of the measurements to be slightly larger than that since the stopwatch itself is somewhat inadequate and there is some small variation in the reaction time of the experimenter which is me.

My value of G was within 5.935% of the theoretical value, but again the range of the experimental values obtained for G does not quite take account of the expected experimental value. These differences are small and can probably be explained by some of the small errors listed above, which were not necessarily accounted for in the uncertainty calculations. Hence my result seem to be in agreement with existing theory, but in order to determine this for certain, I would need to do further investigation, attempting to control some of these variables.





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Proverb
Explanation / Meaning

A
Absence makes the heart grow fonder. When you are away from someone you love, you love them even more.
Accidents will happen. Some unfortunate events must be accepted as inevitable.
Actions speak louder than words. What a person actually does is more important that what they say they will do.
Advice is cheap.
Advice is least heeded when most needed. When a problem is serious, people often do not follow the advice given.
Advisers run no risks.
All cats are grey in the dark. People are undistinguished until they have made a name.
All that glitters is not gold. Appearances can be deceptive.
All days are short to Industry and long to Idleness. Time goes by slowly when you have nothing to do.
All is fair in love and war Things that are done in love or war can often be excused.
All's well that ends well There is a solution to everything even though there are doubts.
All things grow with time - except grief. As time goes by, grief subsides little by little.
All things are difficult before they are easy.
All work and no play makes Jack a dull boy. Everybody needs a certain amount of relaxation. It is not good to work all
the time.

An apple a day keeps the doctor away.* Eating an apple every day can help to keep you healthy.
Other interpretation : A small preventive treatment wards off serious problems.
An empty purse frightens away friends. When one's financial situation deteriorates, friends tend to disappear.

An Englishman's home is his castle. An Englishman's home is a place where he feels safe, enjoys privacy
and can do as he wishes.
An idle brain is the devil's workshop. When you work you avoid temptation.
An onion a day keeps everyone away.*
An ounce of prevention is worth a pound of cure. It is easier to prevent something from happening than to repair the damage or
cure the disease later.
April showers bring May flowers.

A bad tree does not yield good apples.
A bad workman blames his tools. Blaming the tools for bad workmanship is an excuse for lack of skill.
A bird in hand is worth two in a bush. It's better to keep what you have than to risk losing it by searching for something better.
A broken friendship may be soldered but will never be
sound. Friendships can be rebuilt after a dispute but will never be as strong as before.
A burden of one's own choice is not felt. Something difficult seems easier when it is done voluntarily.
A burnt child dreads the fire. A bad experience will make people stay away from certain things.
A cat has nine lives. 1) Cats can survive many accidents because they land on their feet without injury.
2) Three lives = 3 years to play, 3 years to stray, 3 years to stay.
A chain is no stronger than its weakest link. The strength of a group depends on each individual member.
A change is as good as a rest.
A dry March, a wet April and a cool May
fill barn and cellar and bring much hay.
A fault confessed is half redressed. Confession is the beginning of forgiveness.
A fool and his money are soon (easily) parted. A foolish person usually spends money carelessly.
A friend in need is a friend indeed. Someone who helps you when you are in trouble.
A friend to all is a friend to none. Someone who is a friend to everyone makes none of them feel special.
A good beginning makes a good end. If a task is carefully planned, there's a better chance that it will be done well.

A good conscience is a soft pillow. You sleep well when you have nothing to feel guilty about.
A guilty conscience needs no accuser.
A leopard cannot change its spots. It is not possible for a bad or unpleasant person to become good or pleasant.
A loaded wagon makes no noise. Really wealthy don't talk about money.
A loveless life is a living death.
A man can die but once.
A man is as old as he feels himself to be.

A man is known by the company he keeps. A person's character is judged by the type of people with whom they spend
their time.
A rising tide lifts all boats. Describes something that will be helpful to all.
A rolling stone gathers no moss. If a person keeps moving from place to place, they gain neither friends nor
possessions.
Another interpretation is that, by moving often, one avoids being tied down!
A rotten apple spoils the barrel. A dishonest or immoral person can have a bad influence on a group.
A smooth sea never made a skilled mariner. Overcoming adversity leads to competence.
A stitch in time saves nine. It's better to deal with a problem at an early stage, to prevent it from getting
worse.
A stumble may prevent a fall. Correcting a small mistake may help you to avoid making a bigger one.
A swallow does not make the summer. One good event does not mean that everything is alright.
A tree is known by its fruit. A man is judged by his actions.
A young idler, an old beggar. If you don't work, you won't have any money when you're old.
After dinner rest a while, after supper walk a mile.

B Bad news travels fast. People tend to circulate bad news (accidents, illness etc.) very quickly.

Beauty is only skin deep. A person's character is more important than their appearance.

Beauty is in the eye of the beholder. Different people have different tastes.

Beauty is the wisdom of women. Wisdom is the
beauty of men.

Be swift to hear, slow to speak. Listen carefully before speaking.

Better be alone than in bad company. Be careful in the choice of the people you associate with.

Better flatter a fool than fight him. It's better to avoid disputes with stupid people.

Better the devil you know than the devil you don't
know It's better to deal with somebody difficult but familiar, than change and risk dealing
with somebody worse.

Better late than never. It's better to do something, even if it's late, than not do it at all.

Better lose the saddle than the horse. It's better to stop and accept a small loss, rather than continue and risk losing
everything.

Better untaught than ill-taught It's better not to be taught at all than to be taught badly.
Birds of a feather flock together. People of the same sort are usually found together.

Blood is thicker than water Family relationships are stronger than relationships with other people.
Blood will out. A person's background or education will eventually show.

C Charity begins at home. A person's first duty is to help and care for his own family.
Children and fools tell the truth.
Cleanliness is next to godliness. A clean body is just as important as a pure soul.
Clear moon, frost soon. If the atmosphere is clear, frost may form.
Clothes don't make the man. Appearances can be deceiving.
Constant occupation prevents temptation. When you work you avoid temptation.

D
Dead men tell no tales A dead person cannot cause difficulties by revealing something that it would be preferable to conceal.
Diamond cuts diamond. Refers to two people equally matched in wit or cunning.
Diligence is the mother of good fortune. Hard work brings rewards.
Discretion is the better part of valour It is useless to take unnecessary risks.
Diseases of the soul are more dangerous than
those of the body.

Distance makes the heart grow fonder. When you are separated from the person you love, your feelings are even stronger.
Dogs of the same street bark alike. People from the same background have the same behaviour.

Don't bark if you can't bite. Don't complain if you can't enforce your point of view.
Don't count your chickens before they're hatched. You must not be too confident that something will be successful.
Don't dig your grave with your own knife and fork. Don't do something yourself which causes your own downfall.
Don't judge a book by its cover. Don't judge by appearances.

E
Early to bed and early to rise makes a man healthy,
wealthy and wise.
Easier said than done. What is suggested sounds easy but it is more difficult to actually do it.
Empty vessels make the most noise. The least intelligent people are often the most talkative or noisy.
Every man is the architect of his own fortune.
Every path has its puddle. Progress is rarely without difficulty.
Every why has a wherefore. There is an explanation for everything.
Everything in the garden is rosy. Everything is satisfactory.
Experience is the father of wisdom. Experience and knowledge result in better judgement.


F Facts speak louder than words. People show what they are really like by what they do, rather than by what
they say.

Failure teaches success.
False friends are worse than open enemies.
Familiarity breeds contempt Knowing somebody very well may lead to a lack of respect for them.
Fool me once, shame on you;
fool me twice, shame on me. One should learn from one's mistakes.
Fools rush in where angels fear to tread Inexperienced people act in situations that more intelligent people would avoid
Friendship is love with understanding.

G Give someone an inch and they will take a mile. Give someone a little and they will want more - some people are never satisfied.
Give someone enough rope and they will hang
themselves. Give someone enough time and freedom and they will get into trouble.
God helps those who help themselves.

Good and quickly seldom meet. A well-done job takes time.
Good management is better than good income.
Great minds think alike.

Great oaks grow from little acorns. Large successful operations can begin in a small way.
Grief divided is made lighter

H Half a loaf is better than none. You should be grateful for something, even if it's not as much as you wanted.
Haste makes waste. If something is done too quickly, it may be done carelessly and need to be redone.
Hatred is a blind as love. A person who feels hatred does not see any qualities in the person he/she hates.
He has enough who is content.
He who knows nothing, doubts nothing. Knowledge leads us to make choices.
He who pays the piper calls the tune. The person who provides the money for something should control how it is spent
He who plays with fire gets burnt. If you behave in a risky way, you are likely to have problems.

He laughs best who laughs last. Don't express your joy, or your triumph, too soon!
Health is better than wealth.

Home is where the heart is. You call home the place where the people you love are.
Honesty is the best policy.
Honey catches more flies than vinegar. You can obtain more cooperation from others by being nice.

I
In times of prosperity friends are plentiful. You have many friends when you have no difficulties.
If a camel gets his nose in a tent, his body will
follow. If you let something intrusive enter your life, your life will become difficult .

If in February there be no rain, 'tis neither good
for hay nor grain.
If you are patient in one moment of anger,
you will avoid 100 days of sorrow.
If you chase two rabbits, you will not catch either
one. If you try to do two things at the same time, you won't succeed in doing either of them.
If you want a friend, be a friend.
Ignorance is bliss. Possible interpretation: What you do not know causes no worry or sadness.
In for a penny, in for a pound. If you start something, it's better to spend the time or money necessary to complete it.
In the land of the blind, the one-eyed man is king.
It never rains but it pours. Misfortunes usually come in large numbers.
It is always darkest before the dawn The most difficult time is just before a problem is solved.
It's no use crying over spilt milk. Don't express regret for something that has happened and cannot be remedied.
It takes all sorts to make a world. People vary in character and abilities, and this is a good thing.

K Knowledge in youth is wisdom in age.

Knowledge is power.
Kill the goose that lays the golden egg. Destroy something that would be a source of wealth or success.
Kindness begets kindness. If you are kind to people, they will be kind to you.


L
Learn to walk before you run. Don't rush into doing something until you know how to do it.
Learning is a treasure that will follow its owner
everywhere. Education is something you keep forever.
Let bygones be bygones. Let's forgive and forget past quarrels.
Liars need good memories.
Lightning never strikes in the same place twice An unusual event is not likely to occur again in exactly the same circumstances.
Like father, like son. A son's character can be expected to resemble his father's.
Look before you leap. Consider possible consequences before taking action.
Loose lips sink ships. Disclosing important information ( to the enemy or a competitor) could result in large
losses.
Love is blind. A person in love does not see the faults of the person he/she loves.

M
Make a silk purse out of a sow's ear Manage to produce something good using poor material.
Man is the head of the family;
woman is the neck that turns the head.
Man proposes, God disposes. Our destiny depends on God's will.
Manners make the man. Possibly: a person's manners show their origins.
Many hands make light work. Sharing work makes work easier.
Marry in haste, repent at leisure. If you get married too quickly, you may spend all your life regretting it.

Memory is the treasure of the mind.
Men make houses, women make homes.

Might as well be hanged for a sheep as (for) a lamb If the penalty is going to be the same, you might as well commit the greater offence.
Money begets money. If you have money you can make more money.
Money is the root of all evil. Money is the main cause of wrongdoing and problems.

N
Necessity is the mother of invention. The need for something forces people to find a way of obtaining it.
Never put off till tomorrow what can be done today Don't postpone something you can do now.
Never say die. Never give up.
Nobody is perfect.
No man is an island. We all need other people.
No news is good news. If the news was bad, we would hear of it. Since we have heard nothing,
we can assume that all is well.
Nothing ventured, nothing gained. You cannot expect to achieve anything if you don't take risks.

O Once bitten, twice shy. After an unpleasant experience, people are careful to avoid something similar.
One good turn deserves another. You should be helpful to someone who helps you.
One of these days is none of these days. 'One of these days' remains vague.
One today is worth two tomorrow. What you have today is better than what is promised or hoped for.

One man's meat is another man's poison People don't always like the same things.
Only real friends will tell you when your face is
dirty. Only a real friend will tell you the truth.
Opportunity seldom knocks twice. Don't miss opportunities that come along.
Out of sight, out of mind. We tend to forget people who are absent.


P Penny wise, pound foolish. Refers to a person who is careful about spending small amounts of money, but
not careful about spending large amounts of money.
People who live in glass houses should not throw
stones. One should not criticize others for faults similar to one's own.
Practice makes perfect. Doing something repeatedly is the only way to become good at it.

Practise what you preach Do yourself what you advise others to do.
Prevention is better than cure It is easier to prevent something from happening than to repair the damage or cure the
disease later.

Pride comes before a fall. Don't be too self-confident or proud; something may happen to make you look foolish.
Procrastination is the thief of time Delaying an action for too long is a waste of time.
Put all your eggs in one basket Risk everything by relying on one plan (by putting all one's money in one business).

R Revenge is sweet. There is satisfaction in returning an injury.
Rome was not built in a day. It takes a long time to do a job properly. You should not expect to do it quickly.

S
Save me from my friends. Friends can be more dangerous than enemies.

Saying is one thing, doing is another. People don't always do what they announce.

Short reckonings make long friends. Debts paid quickly encourage friendship.
Sickness in the body brings sadness to the mind.

Snug as a bug in a rug. Feeling very comfortable.
Spare the rod and spoil the child If you don't punish a child when he does wrong, you will spoil his character.
Sticks and stones will break my bones but names
will never hurt me Physical attacks may harm me, but cruel words will not.

Still waters run deep. A quiet person can have much knowledge or wisdom.
A stitch in time saves nine It's better to deal with a problem in its early stages, because if you don't, it will get
worse.
Stolen fruit is the sweetest. What is forbidden is the most tempting.

T Tall oaks grow from little acorns. Great things may come from small beginnings.

The apple doesn't fall far from the tree. Children resemble their parents.
The best advice is found on the pillow. After a good night's sleep we may find an answer to our problem.

The devil looks after his own. Success comes to those who deserve it least .

The devil makes work for idle hands People who have no work, or are idle, often get into or make trouble.
The die is cast. A decision has been made and it's impossible to change it.
The early bird catches the worm. If you want to do something successfully, you should do it as soon as you can.
The end justifies the means. Wrong or unfair methods may be used if the result of the action is good.
The more haste, the less speed. A person makes more progress if they do things less quickly.
The more you have, the more you want.

The pen is mightier than the sword Words and communication have greater effect than war and fighting.
The proof of the pudding is in the eating. The real value of something can be judged only after it has been tried or tested.
The road to hell is paved with good intentions. It's not enough to intend to do something, you must actually do it.
The tongue wounds more than a lance. Insults can be more hurtful than physical injuries.
The truth is in the wine. People speak more freely under the influence of alcohol.
The wish is father to the thought. You think that something is true because you want it to be so.

There is no fool like an old fool. A older person is expected to behave more sensibly.
There is safety in numbers Being in a crowd makes you feel more confident.
Time and tide wait for no man. No one can delay the passing of time.
Time has wings. Time goes by quickly.

Time is money. Time is valuable and should not be wasted.
To err is human, to forgive divine It is human nature to make mistakes, therefore one should forgive.
Too many cooks spoil the broth. If too many people are involved in something, it will not be done properly.

Trust not a horse's heel nor a dog's tooth.
Truth is stranger than fiction. Events in real life are sometimes stranger than in fiction.
Two wrongs don't make a right It is wrong to harm someone because they have harmed you.

U
Union is strength.

V
Variety is the spice of life. Doing a lot of different things makes life more interesting.

Virtue is its own reward. You should not expect praise for acting in a correct or moral way.

W Walls have ears. Be careful. People could be listening.
Waste not, want not. If you never waste anything, you will have it when you need it.
What the eye doesn't see, the heart doesn't grieve
over. If a person doesn't know about something, it cannot hurt them.
What a man says drunk, he thinks sober. People speak more freely under the influence of alcohol.

What soberness conceals, drunkenness reveals. People are less discreet under the influence of alcohol.
When the cat's away, the mice play. People misbehave when their boss, or the person in authority, is absent.

When in Rome, do as the Romans do. You should adopt the customs of the people or country you are visiting,
and behave in the same way.
When poverty come in the door, love goes out the
window.
Where there's life there's hope.

Where there's a will, there's a way. A person with determination will find a way of doing something.
Who makes himself a sheep will be eaten by the wolves. Possible interpretation: an easily influenced person can be mislead.
Wisdom is better than strength.
Wonders will never cease! Expresses surprise at an unexpected pleasure or event (ironic).

Y
You are what you eat.
You scratch my back and I'll scratch yours. You help me and I'll help you.