This article is about pendulums. For the band, see Pendulum (band). For other uses, see Pendulum (disambiguation). "Simple gravity pendulum" assumes no air resistance and no friction.| An animation of a pendulum showing the velocity and acceleration vectors (v and A).| | A pendulum is a weight suspended from a pivot so that it can swing freely.[1] When a pendulum is displaced from its resting equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force combined with the pendulum's mass causes it to oscillate about the equilibrium position, swinging back and forth. The time for one complete cycle, a left swing and a right swing, is called the period. A pendulum swings with a specific period which depends (mainly) on its length. From its discovery around 1602 by Galileo Galilei the regular motion of pendulums was used for timekeeping, and was the world's most accurate timekeeping technology until the 1930s.[2] Pendulums are used to regulate pendulum clocks, and are used in scientific instruments such as accelerometers and seismometers. Historically they were used as gravimeters to measure the acceleration of gravity in geophysical surveys, and even as a standard of length. The word 'pendulum' is new Latin, from the Latin pendulus, meaning 'hanging'.[3] The simple gravity pendulum[4] is an idealized mathematical model of a pendulum.[5] [6] [7] This is a weight (or bob) on the end of a massless cord suspended from a pivot, without friction. When given an initial push, it will swing back and forth at a constant amplitude. Real pendulums are subject to friction and air drag, so the amplitude of their swings declines. Contents[hide] * 1 Period of oscillation * 2 Compound pendulum * 3 History * 3.1 1602: Galileo's research * 3.2 1656: The pendulum clock * 3.3 1673: Huygens' Horologium Oscillatorium * 3.4 1721: Temperature compensated pendulums * 3.5 1851:Foucault pendulum * 3.6 1930: Decline in use * 4 Use for time measurement * 4.1 Clock pendulums * 4.2 Temperature compensation * 4.2.1 Mercury pendulum * 4.2.2 Gridiron pendulum * 4.2.3 Invar and fused quartz * 4.3 Atmospheric pressure * 4.4 Gravity * 5 Accuracy of pendulums as timekeepers * 5.1 Q factor * 5.2 Escapement * 5.3 The Airy condition * 6 Gravity measurement * 6.1 The seconds pendulum * 6.2 Early observations * 6.3 Kater's pendulum * 6.4 Later pendulum gravimeters * 7 Standard of length * 7.1 Early proposals * 7.2 The metre * 7.3 Britain and Denmark * 8 Other uses * 8.1 Seismometers * 8.2 Schuler tuning * 8.3 Coupled pendulums * 8.4 Religious practice * 8.5 Execution * 9 See also * 10 External links * 11 Further reading * 12 References| [edit] Period of oscillation

Main article: Pendulum (mathematics)
The period of swing of a simple gravity pendulum depends on its length, the local strength of gravity, and to a small extent on the maximum angle that the pendulum swings away from vertical, θ0, called the amplitude.[8] It is independent of the mass of the bob. If the amplitude is limited to small swings, the period T of a simple pendulum, the time taken for a complete cycle, is:[9]

where L is the length of the pendulum and g is the local acceleration of gravity. For small swings, the period of swing is approximately the same for different size swings: that is, the period is independent of amplitude. This property, called isochronism, is the reason pendulums are so useful for timekeeping.[10] Successive swings of the pendulum, even if changing in amplitude, take the same amount of time. This formula is strictly accurate only for tiny infinitesimal swings. For larger amplitudes, the period increases gradually with amplitude so it is longer than given by equation (1). For example,...

...Pendulum
From Wikipedia, the free encyclopedia
For other uses, see Pendulum (disambiguation).
"Simple gravity pendulum" model assumes no friction or air resistance.
A pendulum is a weight suspended from a pivot so that it can swing freely.[1] When a pendulum is displaced sideways from its resting equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force combined with the pendulum's mass causes it to oscillate about the equilibrium position, swinging back and forth. The time for one complete cycle, a left swing and a right swing, is called the period. The period depends on the length of the pendulum, and also to a slight degree on the amplitude, the width of the pendulum's swing.
From its examination in around 1602 by Galileo Galilei, the regular motion of pendulums was used for timekeeping, and was the world's most accurate timekeeping technology until the 1930s.[2] Pendulums are used to regulate pendulum clocks, and are used in scientific instruments such as accelerometers and seismometers. Historically they were used as gravimeters to measure the acceleration of gravity in geophysical surveys, and even as a standard of length. The word 'pendulum' is new Latin, from the Latin pendulus, meaning 'hanging'.[3]
The simple...

...Course: Pendulum Measurements
Unit # 1 Lesson # 1
Does the Length of the Pendulum affect the number of swings ?
Materials:
• string ,tape ,washer
• Stop watch
• Meter stick, paper ,pencil
Introduction :
I am doing a study to find out if the length of a Pendulum will affect the number of swings. We usually see pendulums in Grandfather clocks. It is the weight that swings back and forth. I will be changing the length of the string ,but never the weight .
Hypothesis:
I am going to say, that while doing this experiment that as the length of the string decreases , the speed of the pendulum will increase.
Procedure:
1. Got my string and measured the lengths . I marked the string at 80c ,70cm, 60cm all the way to 30 cm. This makes it easier to keep working .
2. Find a table that has a hang over on the side. This way the pendulum can swing freely.
3. Tape the string to the top of the table. Tie a knot at the end of the string and place the washer in the knot.
4. Get someone to help you with the stop watch. Set it for one minute. Now, pull the string back at 10 cm and let go. Do not push the pendulum just let it go freely. Count the complete swings out and back makes one complete swing.
5. Write down the number of swings per minute.
6. Contiunue until you have reached the 30 cm mark .
Data:
The...

...Report : Experiment One
Title: Determination of the acceleration due to gravity with a simple pendulum
Introduction and Theory: A simple pendulum performs simple harmonic motion, i.e. its periodic motion is defined by an acceleration that is proportional to its displacement and directed towards the centre of motion. It can be shown that the period T of the swinging pendulum is proportional to the square root of the length l of thependulum: T2= (4π2l)/g
with T the period in seconds, l the length in meters and g the gravitational acceleration in m/s2. Our raw
data should give us a square-root relationship between the period and the length. Furthermore, to find an accurate value for ‘g’, we will also graph T2 versus the length of the pendulum. This way, we will be
able to obtain a straight-line graph, with a gradient equal to 4π2g–1.
Procedure: Refer to lab manual.
Measurement / Data:
Length of Pendulum ( l +/- 0.1 cm) | Time for 20 Oscillations (s) | Time for 1 Oscillation (Periodic Time) T (s) | T^2 ( s^2) |
| 1 | 2 | Mean | | |
35 | 24.00 | 23.87 | 23.94 | 1.20 | 1.43 |
45 | 26.50 | 26.75 | 26.63 | 1.33 | 1.77 |
55 | 29.94 | 29.81 | 29.88 | 1.49 | 2.23 |
65 | 32.44 | 32.31 | 32.38 | 1.62 | 2.62 |
75 | 35.06 | 35.00 | 35.03 | 1.75 | 3.07 |
85 | 37.06 | 36.87 | 36.97 | 1.85 | 3.42 |
95 | 39.25 | 39.19 | 39.22 | 1.96 | 3.85 |
Length of...

...EXPERIMENT 2 Measurement of g: Use of a simple pendulum
OBJECTIVE: To measure the acceleration due to gravity using a simple pendulum.
Textbook reference: pp10-15
INTRODUCTION:
Many things in nature wiggle in a periodic fashion. That is, they vibrate. One such example is a simple pendulum. If we suspend a mass at the end of a piece of string, we have a simple pendulum. Here, the to and fro motion represents a periodic motion used in times past to control the motion of grandfather and cuckoo clocks. Such oscillatory motion is called simple harmonic motion. It was Galileo who first observed that the time a pendulum takes to swing back and forth through small distances depends only on the length of the pendulum The time of this to and fro motion, called the period, does not depend on the mass of the pendulum or on the size of the arc through which it swings. Another factor involved in the period of motion is, the acceleration due to gravity (g), which on the earth is 9.8 m/s2. It follows then that a long pendulum has a greater period than a shorter pendulum.
Before coming to lab, you should visit the following web site: http://www.myphysicslab.com/pendulum1.html This simulation shows a simple pendulum operating under gravity. For small oscillations the pendulum is linear, but it is non-linear for larger...

...Physics Investigation: What factors affect the period of a pendulum?
By Tanya Waqanika
In this investigation, I will be looking at which factors affect the period (The time for one complete cycle, a left swing and a right swing) of a pendulum (a weight that dangles from a pivot so that it can swing freely). I will do this by tying a metal bob to a length of spring and dropping it from a certain height and measuring the time it takes to complete an oscillation, changing a variable for each of my preliminary investigations.
Independent Variable | Dependent Variable | Control Variables |
Length of String (continuous) | Period of the pendulum (continuous) | Diameter of Bob |
| | Type of Bob |
| | Angle bob dropped from |
| | Person stopping stopwatch |
| | Person dropping bob |
| | Height Bob is dropped from |
Preliminary Investigations
Preliminary One: Length of Strong
Results Table
| Time of Period (seconds) |
Length of String | Trial 1 | Trial 2 | Trial 3 | Ranges | Averages (mean) |
10cm | 0.87 | 0.69 | 0.87 | 0.69-0.87 | 0.81 |
20cm | 1.01 | 1.02 | 1.01 | 1.01-1.02 | 1.01 |
30cm | 1.32 | 1.42 | 1.32 | 1.32-1.42 | 1.35 |
40cm | 1.66 | 1.71 | 1.66 | 1.66-1.71 | 1.68 |
According to my graph, there is a positive correlation between the period of a pendulum and the length of string, meaning that as...

...Is gravity always 9.8m/s2??
INTRODUCTION: A simple pendulum consists of a mass m swinging back and forth along a circular arc at the end of a string of negligible mass. A pendulum is a weight suspended from a pivot so that it can swing freely. Gravity is the pull that two bodies of mass exert on one another. There are several simple experiments that will allow you to calculate the acceleration due to gravity of a falling object. A simple pendulum can determine this acceleration. The only variables in this experiment are the length of the pendulum (L) and the period of one full swing of the pendulum (T). In this case the independent variable represents the length of the string and the dependent variable represents the period of one oscillation. The control variable is the mass of the pendulum. In this lab our goal was to see if we can prove if the acceleration due to gravity is 9.8m/s2. The R2 in this lab is closed to 9.8 m/s2 . The formula that we used in this lab is T=2πLg and then we solved for g=L(T2π)2.
HYPOTHESIS: The gravity will be 9.81 m/s2 at sea level due to the acceleration.
PROCEDURE:
Materials: stopwatch, meter stick, support stand, string, mass (200g), rod clamp, protractor.
Safety: Be careful not to drop any of the heavy materials or to hit somebody near you by using them.
1. Set up the support stand on a flat surface.
2. Tie to mass at the end of the string...

...UNIVERSITY OF TRINIDAD AND TOBAGO
Point Lisas Campus, Esperanza Road, Brechin Castle,
Couva, Trinidad, W.I.
Program: National Engineering Technician Diploma
Course code: ENSC 110D
Class: Petroleum
Lab Title: Pendulum with a yielding support
Instructor: Mrs. Sharon Mohammed
Full time
Name: Kirn Johnson
Student ID: 58605
Date: 28/10/2012
Title
A Pendulum with a yielding support
Table of Contents
1. Abstract
2. Objectives
3. Theory
4. Apparatus / Materials
5. Procedure / Method
6. Results / data
7. Analysis / Data
8. Conclusion
9. Reference
Abstract
Intent: To conduct an experiment to prove the yielding support distance is directly proportional to the period.
Results:
d(m) | Time for 20 Oscillations (s) | Time for 1 Oscillation T (s) | T2(s2) | d3(m2) x 10-3 |
| 1 | 2 | 3 | Average | | | |
0.24 | 31.50 | 31.47 | 31.44 | 31.47 | 1.57 | 2.46 | 13.8 |
0.21 | 31.0 | 30.97 | 31.09 | 31.02 | 1.55 | 2.41 | 9.2 |
0.l8 | 30.56 | 30.69 | 30.69 |...

...HSC PHYSICS
2011
HSC PHYSICS
2011
PENDULUM MOTION
BY NATHAN LOCKE
Image taken from http://www.practicalphysics.org/go/Experiment_480.html
Pendulum Motion
Aim: To determine the rate of acceleration due to gravity by using a pendulum.
Background Information:
Equation One:
T=2πlg
Where
T = the period of the pendulum (s). This is the time taken for the pendulum to return to its starting position.
l = length of the pendulum
g = the rate of acceleration due to gravity (ms-2)
* In order to find the acceleration due to gravity, the equation must be rearranged to look like this, and give “g” as the subject:
g=4π2lT2
Procedure:
1. Mass to stop the stand falling over
Mass to stop the stand falling over
Protractor (attached)
Protractor (attached)
Bosshead
Bosshead
Retort Stand
Retort Stand
Mass
Mass
String
String
Clamp
Clamp
In a group of 2, we set up the apparatus shown below:
2. We measured the length of the pendulum from the base of the mass to the swinging point on the clamp. We recorded this length in our table.
3. We moved the position of the pendulum to 27° from the vertical.
4. We released the pendulum, and recorded the time taken for ten complete oscillations using a stopwatch.
5. We reduced the length of the pendulum by approximately 8cm and repeated steps two to five,...