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Pendulum. 82 劉威宏 83 劉致毅 86 劉書君 89 賴勇仁 . Pendulum. A gravity pendulum is a weight on the end of a rigid or flexible line or rod, which, when given some initial lift from the vertical position, will swing back and forth under the influence of gravity over its central (lowest) point.

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82 劉威宏83劉致毅

86 劉書君 89賴勇仁


  • A gravity pendulum is a weight on the end of a rigid or flexible line or rod, which, when given some initial lift from the vertical position, will swing back and forth under the influence of gravity over its central (lowest) point.

  • A torsion pendulum consists of a body suspended by a fine wire or elastic fiber in such a way that it executes rotational oscillations as the suspending wire or fiber twists and untwists.

Galileo galilei
Galileo Galilei

  • "The legend of how Galileo discovered this property of the simple pendulum is apocryphal, but neither the fact that he found it nor the profound effects that it had on our civilization can be denied.“

  • 1.Telescope

  • 2.Pendulum


  • In 1637, Galileo demonstrated the first pendulum as a controller for clock

  • Control by gravity

  • Pendulum has a natural frequency that is independent of amplitude and weight of the bob

  • Its frequency is related only to length of the pendulum and acceleration of gravity.


  • Complete the task of Hipparchos which is to use planet as timekeeper.

  • -- use the four moons of Jupiter, with the added advantage that the eclipse occurs once or twice every night.


  • --telescope is impossible to use at sea.

  • --the eclipses were not quite instantaneous.


  • the second contribution to longitude story, and a significant contribution to horology

  • 1484 Bernard Walther measure the interval between the rising of the planet Mercury and moment of sunrise.

  • Tycho Brahe purchased and tried four clocks during 1577 and 1581 before concluding that the inherent defects of sixteenth century clockwork were too great for astronomical purposes.

Galileo s first pendulum
Galileo’s first pendulum

  • At the age of 19 when Galileo was at a church and observed a chandelier swinging.

    suspension light

    He timed the length of the pendulum's swing, or oscillation, with his pulse and made an interesting discovery.

No matter how far the chandelier swung, the length of time it took for one oscillation was always the same.


  • Isochronism

  • Period T=2

  • Associated with length, not with gravity

  • It is isochronism that cause horology development

Pendulum clock
Pendulum clock

  • Invented by Galileo Galilei and his son, Vicenzio.

  • First patented by Christiaan Huygens in 1657.

  • Pendulum clocks have several parts:

  • Pendulums are made to not vary in length when the temperature changes.

  • Solution --John Harrison invented the grid pendulum, which used the differential expansion of brass and steel to achieve a zero-expansion pendulum.

  • Pendulums are frequently polished and streamlined to reduce the randomizing effects of turbulent air flow on the clock's accuracy.

  • Solution--In the late 19th century and early 20th century, pendulums for clocks in astronomical observatories were often operated in a vacuum to make the pendulum's operation even more accurate.

Christina huygens
Christina Huygens

  • in 1657, invented the first weight-driven clock with a pendulum

Make string oscillating along with the same cycloid

To reduce error

John harrison 1693 1776
John Harrison(1693-1776)

  • He was given a watch when he was six to amuse him while in bed with smallpox, spending hours listening to it and studying its moving parts

  • Developed the gridironpendulum, consisting of alternating brass and steel rods assembled so that the different expansion and contraction rates cancelled each other out.

  • The grasshopper escapement -- a control device for the step-by-step release of a clock's driving power.

Gridiron pendulum
Gridiron pendulum

  • The gridiron pendulum was an improvement of clocks developed by John Harrison, consisting of alternating brass and steel rods assembled so that the different expansion and contraction rates cancelled each other out.

  • Any downward expansion of the suspended steel is counteracted by the upward expansion of the supporting brass. The adjustable pin connection was designed to make minute alterations to the length, in the field.

Spring driven clocks early 15th century europe
Spring-driven clocks (Early 15th century, Europe)

  • Spring-driven clocks brought timekeepers out of towers and into the home. In contrast to their weight-driven predecessors, spring-driven clocks are small and portable.

  • Lead to the development of the first watch in the 15th century.

Mechanical clock c 1270s probably europe
Mechanical clock (c,1270s, probably Europe)

  • the driven weight is suspended from a cord wound around the main gear shaft, or barrel. As gravity pulls the weight down, the barrel turns, thus driving the escape wheel.

  • In a typical verge-and-foliot escapement, the weighted rope unwind from the barrel, turning the toothed escape wheel.

  • Escapement stabilize the power of gravitational force.

Pendulum clock 1656 dutch astronomer christian huygens
Pendulum clock(1656, Dutch astronomer Christian Huygens)

  • In the early 1580s, Galileo observed that a given pendulum took the same amount of time to swing completely through a wide arc as it did a small arc.

  • 1656 Huygens combined pendulum with a particular kind of escapement.

  • Weight-driven Spring-driven

  • In 1906, the first pendulum clock driven by a self contained battery started ticking.

H1 1730 1735

  • a portable version.

  • It is spring-driven and only runs for one day.

  • The moving parts are controlled and counterbalanced by springs so that, H1 is independent of the direction of gravity.

  •  It ensures that any change in motion which affects one of the balances is compensated for by the same effect on the other balance.

H2 1737 1740

  • Fundamentally the same design as H1.

  • Harrison began work on H2 in 1737 but in 1740 realised its design was wrong.

  • The bar balances did not always counter the motion of a ship, a deficiency that could be corrected if the balances were circular.

  • Harrison requested more money from the Board to work on a third timekeeper...

H3 1740 1759

  • After 19 years of labour, it failed to reach the accuracy required by the Board of Longitude

  • H3 incorporated two inventions of Harrison's; a bimetallic strip, to compensate the balance spring for the effects of changes in temperature, and the caged roller bearing, the ultimate version of his anti-friction devices.

  • the solution to the longitude problem lay in an entirely different design.

In the end of our report we would like to share with you
In the end of our report, we would like to share with you…

Weep no more , no sigh , nor groan. Sorrow calls no time that's gone

The time of life is short ; to spend that shortness basely, it would be too long .

Do you love life ? Then do not squander time ; for that's the stuff life is made of .

The End