Factors Affecting the Time Period of a Simple Pendulum

7/27/2019 Factors Affecting the Time Period of a Simple Pendulum

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Factors Affecting The Time Period of a Simple Pendulum

I plan to investigate the different characteristics of a simplependulum and the factors affecting its time period.

Any motion that repeats itself in equal intervals of time is calledperiodic motion.

Simple harmonic motion (SHM) also is a periodic motion, but has somefeatures:

It is periodic

Motion is to and fro along a straight line about an equilibrium(mean) position

Acceleration is directly proportional to displacement

Acceleration is directed towards the equilibrium position

Therefore, simple harmonic motion is a periodic motion whereacceleration is directly proportional to displacement, and is alwaysdirected towards the equilibrium position.

Simple Pendulum-

What we call a simple pendulum is a string with a mass tied to the endof it. The mass is called a 'bob'. If we had kept the string with thebob attached to it at a fixed point and then we displace it from thisequilibrium position, the movement of the bob we would see would be ato and fro movement where the bob would move in a straight arced linefrom left to right. The distance of the movement of the pendulum awayfrom the equilibrium position is called its displacement.

(Diagram 1 shows you the basic diagram of what was explained above)

The three different types of oscillations are free, damped and fixedoscillations.

Free oscillations occur while the pendulum, is set to itsdisplacement and is moving in its to and fro motion it doesn'texperience any force that prevents it from continuing this motion.Such forces that prevent free oscillation areair resistance, etc.
http://www.123helpme.com/search.asp?text=simple+pendulumhttp://www.123helpme.com/search.asp?text=air+resistancehttp://www.123helpme.com/search.asp?text=simple+pendulumhttp://www.123helpme.com/search.asp?text=air+resistance


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Damped oscillations occur while the pendulum, is set to itsdisplacement and is moving in its to and fro motion, experiences aforce, or a medium that affects its motion. For example airresistance, water, etc.

A forced oscillation occurs while an object is used to force one ormore pendulums into motion. An example of this is using a drivingpendulum to control the displacement of a set of 4 pendulums, whichmove as a result of the driving pendulum being displaced. Anotherexample is using a vibrating tuning fork to force a stretched stringto vibrate and set the pendulum into motion.

Time period-

The Time Period is the time that is required for one completeoscillation. (T)

Frequency is the number of oscillations per second, which is measuredin hertz (Hz).

Angular Velocity- the angle at which the radius vector subtends at thecenter in one second is called the angular velocity of the particle.Its unit is radians per second. That is, (rad s-1)======================================================================

= (theta) / t = 2 / t

Key:

= omega

(theta) = the angle which is covered

t = the time taken

(Diagram 2 illustrates the simple pendulum using the formulaespecified above)

Suppose that you have a vector quantity, V. Theta is the angle droppedto the horizontal component. Any force can be resolved into a verticalcomponent and a horizontal component.

Cosine Theta = Adjacent / Hypotenuse Sine Theta = Opposite /
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Hypotenuse

Cosine Theta = Adjacent / V Sine Theta = Opposite / V

Adjacent = V (Cosine Theta) Opposite = V (Sine Theta)

In the below diagram, the weight, 'Mg' (mass into gravity), can beresolved into two components. The first component 'Mg cosine'compensates for the tension in the string. 'Mg sine' is the componentthat provides the restoring force. The restoring force is requiredbecause it brings the mass back towards the equilibrium position.

Initially it is a forced oscillation, but after two or threeoscillations, the pendulum is in simple harmonic motion. We take alarge number of oscillations, 10, because it reduces errors, as anyerrors that occur will be minimized.

Factors Affecting Time Period Of A Simple Pendulum--------------------------------------------------

* Length- For the length of the pendulum, we consider the lengthfrom the suspension point of the string to the bottom of the bob,and then subtract the radius. While investigating the length, allother factors must be maintained constant for it to be a fairtest. Therefore, the mass, amplitude and the acceleration due togravity have to be constant. Since the amplitude and the mass willbe constant, the bob will have to displaced by 5cm for the firsttest, and then so on accordingly for the other tests:

Considering the law of energy that is, energy cannot be created ordestroyed, we can say that all the potential energy at the ends willbe transferred to the maximum kinetic energy that exists at theequilibrium position.

Max P.E at extreme ends = Max K.E at the equilibrium position

Mgh = mv2; cancel out mass and multiply by 2 on both sides

2gh = v2

2gh = v

(Below is a diagram showing how the increase in length of string)


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Velocity is independent of the mass of the bob. If you use the samelinear amplitude as before, when the length increases, the height ofdisplacement reduces, the potential energy decreases, so kineticenergy decreases, velocity reduces and as the distance remains thesame, Time Period increases.

* Mass of the bob- The mass of the bob could affect the time period,but the velocity is independent of mass, since we are maintainingthe same linear amplitude, which means that it has the same speedand same distance, and so the time taken for an oscillation is thesame. Therefore, a change in mass won't affect the time period ofa simple pendulum. This is also proven by the fact that in theequation v = 2gh, the mass on both sides of the equation canceleach other out.

* Amplitude- The other factor that could affect the time period of

the bob is its amplitude. To investigate this factor all otherfactors must remain constant. When the amplitude increases, theheight of displacement increases, the potential energy increases,so kinetic energy increases, velocity increases and as thedistance increases, but the Time Period remains the same.

Gravitational field strength- the other factor that might affect thetime period of the bob is gravitational field strength. To investigatethis factor all other factors must remain constant. When thegravitational field strength increases, the potential energyincreases, so kinetic energy increases, velocity increases and as thedistance remains the same, but the Time Period decreases.

Procedure:

List of apparatus:

* Different lengths of string

* Digital stopwatch

* Clamp stand

* Meter ruler

* Bobs (weights) of different masses

The length of the pendulum is the length of the string from thesuspension point of the string to the bottom of the bob, and then the


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radius of the bob has to be subtracted from this amount. Keeping thestring at a longer length than that which is actually required, andthen decreasing the length for each test can adjust length.

For the investigations, I am planning to investigate a minimum of 5

length of string (40cm, 50cm, 60cm, 70cm, 80cm, 80cm, 90cm, etc.). Iam planning to investigate a minimum of 3 different masses for the bobas well (400g, 800g, 1200g, etc.). And finally I am planning toinvestigate a minimum of 3 different amplitudes (6cm, 9cm, 12cm,).

After the bob is set into motion, we must allow a few freeoscillations because initially they are forced oscillations.

If the starting point is taken as the extreme right an oscillation issaid to be complete when the pendulum comes back to that specific side(right).

(Below is a diagram illustrating this)

The Bob moves from the position on the right, past the equilibriumthen to the left, then back again past the equilibrium and then to theright side again. This is one complete oscillation.

This is what the table for the different lengths would look like:

Mass of bob = g

Linear amplitude = cm

Length (cm)

Time for 10 oscillations

Time period

= t / 10

t1 (s)

t2 (s)

Avg. t = t1 + t2 / 2

40


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50

60

70

80

90

100

110

This is what the table for the different masses would look like:

Length = cm

Linear amplitude = cm

Mass (g)


Time period

= t / 10

t1 (s)

t2 (s)

Avg. t = t1 + t2 / 2

400

800

1200

1600


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2000

2400

This is what the table for the different amplitudes would look like:

Mass of bob = g

Length = cm

Amplitude (cm)


Time period

= t / 10

t1 (s)

t2 (s)

Avg. t = t1 + t2 / 2

6

9

12

15

18

Prior Test

First I carried out a prior test using the same procedure as theprocedure explained to see exactly how the experiment works, exceptfor the fact that I was provided with different masses which were notthe ones that I had predicted and I used different linear amplitudesand not the ones that I had predicted, and I had carried out threetests when investigating each factor, not 2 as I had planned.


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I used;

A string of length 50cm

A bob with mass 18g

A bob with radius 0.8cm

The following is the table of results that I ended up with aftercarrying out the experiment:

Amplitude (cm)


Time period

= t / 10

t1 (s)

t2 (s)

t3 (s)

Avg. t = t1 + t2 / 3

5

14.16

14.20

14.14

14.17

1.417

10

14.26

14.12


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14.13

14.17

1.417

15

14.17

14.16

14.22

14.18

1.418

Hence By looking at the above results, I can conclude that mypredictions were correct because the amplitude doesn't affect the timeperiod of the pendulum, when the mass and the length are keptconstant.

(Following is the graphical representation of these results on agraph.)

ASHLEY. FERNANDES=================

2. 3. 2004

SR 5 'B'

PHYSICS CW- FACTORS AFFECTING THE TIME PERIOD OF A SIMPLE PENDELUM

OBTAINING EVIDENCE------------------

After the prior test, I decided to carry out the experiments asdescribed in the procedure, to analyse the length, mass and linearamplitude factors.


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BOB

RADIUS (cm)

MASS (g)

BIG

1.3

65

MEDIUM

1

29

SMALL

0.8

18

These are the results that I had obtained when considering the lengthfactor, where the mass was kept constant at 65g, the radius was 1.3cmand the linear amplitude was kept constant at 15cm:

LENGTH (cm)

TESTS (s)

T = t/10 (s)

First

Second

Thrid

Average

30


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11.22

11.22

11.28

11.24

1.124

40

12.9

13.04

12.92

12.95333

1.29533333

50

14.44

14.5

14.41

14.45

1.445

60

15.75

15.83

15.75

15.77667

1.57766667


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70

17.22

17.03

17.25

17.16667

1.71666667

80

18.91

18.68

18.69

18.76

1.876

90

19.43

19.37

19.37

19.39

1.939

100

20.38

20.62

20.29


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20.43

2.043

110

21.63

21.62

21.5

21.58333

2.15833333

120

22.03

22.19

22.31

22.17667

2.21766667

These are the results that I had obtained when considering the linearamplitude factor, where the mass was kept constant at 65g, the radiuswas 1.3cm and the length was also kept constant at 50cm:

AMPLITUDE (cm)

TESTS (s)

T = t/10 (s)

First

Second

Thrid

Average


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5

14.31

14.25

14.24

14.26667

1.42666667

10

14.34

14.36

14.32

14.34

1.434

15

14.44

14.5

14.41

14.45

1.445

These are the results that I had obtained when considering the massfactor, where the linear amplitude was kept constant at 15cm and thelength was also kept constant at 50cm. The radius for each mass was0.8cm (small bob), 1cm (medium bob) and 1.3cm (big bob) respectively:

MASS (g)

TESTS (s)


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T = t/10 (s)

First

Second

Thrid

Average

Big 65

14.44

14.5

14.41

14.45

1.445

Medium 29

14.2

14.46

14.22

14.29333

1.42933333

Small 18

14.44

14.5

14.41

14.45


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1.445

(Below are the graph done on plotted sheets to show length againsttime, amplitude against time and mass against time)

ASHLEY. FERNANDES=================

2. 3. 2004

SR 5 'B'


ANALYSIS--------

Conclusions:

1. For the graph time period against length we suggest that it isnot a linear graph, instead it is a curve. This is because aslength increases, time period increases. For the same linearamplitude, as length increases the height through which the bobmoves decreases. Hence when height decreases, kinetic energy willdecrease, so also causing potential energy to decrease. Velocitytherefore decreases. As velocity decreases, time period willincreases. Therefore the prediction that I had made in planning isproven right.

2. The graph time period against mass does not affect time period.

Mgh at extreme ends = mv at extreme ends

V = 2gh

Velocity doesn't depend on mass. Distance remains the same, due to thelinear amplitude being constant. So time period remains the same andtherefore mass is not affected by time period.

3. Time period is not affected by change in amplitude. When linearamplitude increases, height through which the bob moves increases.When height increases potential energy and kinetic energy


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From the above equation, g x (- x / l) ; a = g -x / l

x / a = l / g

Therefore, T = 2 l / g

T2 = 42 x l /g

T2 = 42 / g (l)

Hence 42 / g, is a constant

Thus T2 is directly proportional to l

L is directly proportional to T2

Therefore L directly proportional to T2 graph is needed.

Following is a table of the length against time squared. This table isused to find the value for gravity.

Length (m)

T^2 (s)

Gravitational val.

0.3

1.263376

9.37

0.4

1.677888444

9.41

0.5

2.088025

9.45


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0.6

2.489032111

9.52

0.7

2.946944444

9.38

0.8

3.519376

9

0.9

3.759721

9.45

1

4.173849

9.46

1.1

4.658402778

9.32

1.2

4.918045444

9.63

9.399


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Therefore the average gravity value obtained is, 9.399 9.40

I will hence plot a graph for length against time squared for thefollowing values.

Length (cm)

T^2 (s)

30

1.263376

40

1.677888444

50

2.088025

60

2.489032111

70

2.946944444

80

3.519376

90

3.759721

100

4.173849

110

4.658402778


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120

4.918045444

I am going to use the following formula to see if I obtain the right

value for gravity from my graph.

Gradient = T2 ' L

g = 42 x l / T2

Gravitational strength = 42 x 1 / Gradient

Gradient = (2.50 / 0.6) - (1.26 / 0.3) = 1.24 / 0.3 = 4.133

Gravitational strength = 42 / 4.133

= 9.5520

'G' value from table- 9.40

'G' value from graph- 9.55

From the above statements, both values are around the value, 9.8 so Ican conclude that my results were accurate.

Quantitative Conclusions========================

To confirm the accuracy of my results I will investigate further usingquantitative tests.

Sine = A / L

= sin-1 A / L

Cosine = L1 / L = L - h / L

(L Cosine) = L - h

H = L - (L Cosine)

V = x , where 'V' is the velocity, '' is Omega and '' is the


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amplitude

= 2 / T

Kinetic energy = mv2, where 'm' is the mass and 'v' is the velocity.

Gravitational potential energy = M x g x H, where 'M' is the mass, 'g'is the gravity that is found from the table and the graph and 'H' isthe height.

Using the above formulas, I will find the height of displacement,velocity, kinetic energy, and potential energy. I will compare thevalues for kinetic energy and potential energy, and see if they arealmost the same. If they are, then the experiment that I carried outwas accurate.

Following is the calculation as done for the 0.3m strings:

= Sine-1 A / L

= Sine-1 15 / 30

= 30

H = L - (L Cosine)

H = 30 - (30 x cos30)

H = 4.019cm = 0. 0401m

V = x

V = 2 / T x 0.15m

V = 0.838 m/s

Kinetic energy = mv2

= x 0.065 x 0.8382

= 2.282293 x 10-2 J

Gravitational potential energy = Mgh

= 0.065 x 9.8x 0.0401


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= 2.55437 x 10-2 J

Length (L)

(m)

Height

H = L - L Cosine (m)

Velocity

V = x (m/s)

Kinetic Energy

K.E. = mv2 (J)

Potential Energy

P.E. = Mgh (J)

0.3

0.0401

0.838

0.02282293

0.0255437

0.6

0.9

From the above results I find that the values for kinetic energy andpotential energy are quite similar, therefore I can conclude that myresults were accurate. Looking at the table we see that as lengthincreases, velocity decreases therefore the time period is increasing.

ASHLEY. FERNANDES


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=================

4. 3. 2004

SR 5 'B'


EVALUATION----------

After analyzing the results that were obtained, I concluded that myinvestigation on the factors that effect the time period of a simplependulum were correct. This can be established using the variousvalues that were calculated from the results, including the value for

the gravitational force acting on the bob. Moreover, once a pendulumis in simple harmonic motion, the potential energy it has at theextreme ends will be equal to the kinetic energy at its equilibriumposition, due to none of its energy is lost; only instead changed.This was also indicated in the results obtained from the readings forthe Potential energy that was calculated was similar to the value forthe kinetic energy of the bob. From the tables in obtaining andanalysis where we see the observed time period and calculated timeperiod, we notice that there are slight differences in the values forthe Time Period that were obtained and those that were calculatedusing the formula. (T = 2 x / (L / g) [where g = 9.81 N/kg]) However,there is merely a difference of 0.01 of a second in most of thereadings. Furthermore, both results show a general trend that as thelength of the pendulum increases, the time period also increases.Taking this in consideration, I can conclude that my results, and theprocedure itself, were accurate.

I can conclude that though the method is reliable for investigationpurposes, it is not very suitable for obtaining reliable results forcalculation. This is because there is too much scope for human error,as in the recording of the time taken for ten oscillations (parallaxerror), in the measurement of the amplitude of the oscillations, andeven in taking the length of the string for the pendulums created. Tocurtail this margin of error, perhaps pendulums of standard lengthscould be used during the experiment, instead of measuring outdifferent lengths. Also, for measuring the times for the variousoscillations, Infra- red sensors connected to computers could be used,so that the times taken for ten oscillations could be monitored andrecorded precisely.


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mass acting downwards.

Therefore, Mg = K.E

As shown in Figure 3, when the spring is pulled down, it is extended

more by the distance (x). Considering this, the tension of the springacting upwards once it is pulled further can be given by the formula,F = k (e + x)

As the spring is being pulled downwards, there will be a resultantdownward force (causing the spring to move downwards). This resultantdownward force can be calculated using the formula:

Resultant force 'F' (downwards) = Mg - k (e + x)

Since Mg = K.E, the above equation can be formed as,

F = K.E - k (e + x)

Once lengthened, this equation will look as follows:

F = K.E - K.E - KX

F = - KX

Therefore, F = - KX

Since k is a constant, the relationship between the resultantdownwards force and the extension can be written as, F - x

This states that as the resultant downward force increases, theextension of the spring (x) will also increase.

Furthermore, since 'F = -KX' and F = MA (Newton's 2nd Law), a newequation can be formed:

MA = -KX

A = (-k / m) x

'K' and 'M' are both constants, and so they can be replaced by '2,'which is a positive constant. Hence, 2 = k / m

Therefore we get, = (k / m)


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For a SHM the time period = 2 /

Considering the previous equation, I can thus say,

T = 2 / (k / m) otherwise, T = 2 x (m / k)

In this fashion, the Time Period of the spring oscillations can becalculated. Also, the effect of the varying factors, such as using anobject of greater mass, increasing the length of the spring, or evenincreasing the pulling force on the spring, on the Time Period of theoscillation, may perhaps be studied.

Simple PendulumA simple pendulum is one which can be considered to be a point masssuspended from a string or rod of negligible mass. It is a resonant system witha single resonant frequency. For small amplitudes, the period of such a

pendulum can be approximated by:

Show

For pendulum length

L = cm = mand acceleration of gravity

g = m/s 2the pendulum period is

T = s(Enter data for two of the variables andthen click on the active text for thethird variable to calculate it.)

This expression for period isreasonably accurate for angles of a fewdegrees, but the treatment of the largeamplitude pendulum is much more

complex.

If the rod is not of negligible mass, thenit must be treated asa physical pendulum .

Index

Periodicmotion

concepts

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Pendulum MotionThe motion of a simple pendulum is like simple harmonic motion in that theequation for the angular displacement is

Show

which is the same form as the motion of a mass on a spring:

The anglular frequency of the motion is thengiven by

compared to for a mass on a spring.

The frequency of the pendulum in Hz is given by

and the period of motion is then

.

Index

Periodicmotion

concepts

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Period of Simple PendulumA point mass hanging on a massless string is an idealized example of a simple

pendulum . When displaced from its equilibrium point, the restoring force

which brings it back to the center is given by:

Show

For small angles , we can use the approximation

Show

in which case Newton's 2nd law takes the form

Even in this approximate case, the solution of the equationuses calculus and differential equations. The differentialequation is

and for small angles the solution is:

Index

Periodicmotion

concepts

http://hyperphysics.phy-astr.gsu.edu/hbase/pend.html#c1http://hyperphysics.phy-astr.gsu.edu/hbase/pend.html#c1http://hyperphysics.phy-astr.gsu.edu/hbase/pend.html#c1http://hyperphysics.phy-astr.gsu.edu/hbase/torq.html#equihttp://hyperphysics.phy-astr.gsu.edu/hbase/pend.html#c4http://hyperphysics.phy-astr.gsu.edu/hbase/trgser.html#c1http://hyperphysics.phy-astr.gsu.edu/hbase/newt.html#fmahttp://hyperphysics.phy-astr.gsu.edu/hbase/newt.html#fmahttp://hyperphysics.phy-astr.gsu.edu/hbase/pend.html#c5http://hyperphysics.phy-astr.gsu.edu/hbase/pend.html#c5http://hyperphysics.phy-astr.gsu.edu/hbase/pend.html#c5http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/permot.html#permothttp://hyperphysics.phy-astr.gsu.edu/hbase/permot.html#permothttp://hyperphysics.phy-astr.gsu.edu/hbase/permot.html#permothttp://hyperphysics.phy-astr.gsu.edu/hbase/hph.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/hph.html#mechconhttp://history.go%28-1%29/http://hyperphysics.phy-astr.gsu.edu/hbase/pend.html#c1http://hyperphysics.phy-astr.gsu.edu/hbase/pend.html#c1http://hyperphysics.phy-astr.gsu.edu/hbase/torq.html#equihttp://hyperphysics.phy-astr.gsu.edu/hbase/pend.html#c4http://hyperphysics.phy-astr.gsu.edu/hbase/trgser.html#c1http://hyperphysics.phy-astr.gsu.edu/hbase/newt.html#fmahttp://hyperphysics.phy-astr.gsu.edu/hbase/pend.html#c5http://hyperphysics.phy-astr.gsu.edu/hbase/pend.html#c5http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/permot.html#permothttp://hyperphysics.phy-astr.gsu.edu/hbase/permot.html#permothttp://hyperphysics.phy-astr.gsu.edu/hbase/permot.html#permothttp://hyperphysics.phy-astr.gsu.edu/hbase/hph.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/hph.html#mechconhttp://history.go%28-1%29/


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Pendulum Geometry

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Periodicmotion

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http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/permot.html#permothttp://hyperphysics.phy-astr.gsu.edu/hbase/permot.html#permothttp://hyperphysics.phy-astr.gsu.edu/hbase/permot.html#permothttp://hyperphysics.phy-astr.gsu.edu/hbase/hph.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/hph.html#mechconhttp://history.go%28-1%29/http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/permot.html#permothttp://hyperphysics.phy-astr.gsu.edu/hbase/permot.html#permothttp://hyperphysics.phy-astr.gsu.edu/hbase/permot.html#permothttp://hyperphysics.phy-astr.gsu.edu/hbase/hph.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/hph.html#mechconhttp://history.go%28-1%29/


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Pendulum EquationThe equation of motion for the simple pendulum for sufficiently smallamplitude has the form

which when put in angular form becomes

This differential equation is like that for the simple harmonicoscillator and has the solution:

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Periodicmotion

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Pendulums can be of many different types. A simple pendulum consists of a bob or a weighhanging at the end of a string or a wire. When the bob of the pendulum is pulled aside andlet go it swings back and forth under the influence of gravitational force of the Earth. That is,the pendulum starts oscillating.

The path travelled by the bob while oscillating is called the arc of the pendulum. The travel of bob from one end of the arc to the other and back to the original point is called oneoscillation of the pendulum. The time taken for one oscillation is called period of thependulum. I believe when you are saying the speed of the pendulum, you mean number of oscillation of the pendulum in unit time. Higher the speed of the pendulum, higher the

number of oscillation per minute, or lower the period of oscillation.

The period of oscillation of a pendulum is dependent only on two factors - length of thependulum and the gravitational force of the earth. The period increases with the increase inlength, and decreases with increase in gravitational force. The mass of the bob has no effecton speed of the pendulum. Similarly the amplitude of the pendulum - that is the distancebetween two extreme points of the arc - has no impact on speed of the pendulum.
http://hyperphysics.phy-astr.gsu.edu/hbase/pend.html#c1http://hyperphysics.phy-astr.gsu.edu/hbase/rotq.html#rqhttp://hyperphysics.phy-astr.gsu.edu/hbase/diff2.html#c2http://hyperphysics.phy-astr.gsu.edu/hbase/diff2.html#c2http://hyperphysics.phy-astr.gsu.edu/hbase/shm2.html#c2http://hyperphysics.phy-astr.gsu.edu/hbase/shm2.html#c2http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/permot.html#permothttp://hyperphysics.phy-astr.gsu.edu/hbase/permot.html#permothttp://hyperphysics.phy-astr.gsu.edu/hbase/permot.html#permothttp://hyperphysics.phy-astr.gsu.edu/hbase/hph.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/hph.html#mechconhttp://history.go%28-1%29/http://hyperphysics.phy-astr.gsu.edu/hbase/pend.html#c1http://hyperphysics.phy-astr.gsu.edu/hbase/rotq.html#rqhttp://hyperphysics.phy-astr.gsu.edu/hbase/diff2.html#c2http://hyperphysics.phy-astr.gsu.edu/hbase/shm2.html#c2http://hyperphysics.phy-astr.gsu.edu/hbase/shm2.html#c2http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/permot.html#permothttp://hyperphysics.phy-astr.gsu.edu/hbase/permot.html#permothttp://hyperphysics.phy-astr.gsu.edu/hbase/permot.html#permothttp://hyperphysics.phy-astr.gsu.edu/hbase/hph.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/hph.html#mechconhttp://history.go%28-1%29/


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The gravitational force of the earth at any place remains constant. Therefore at any givenplace the period of the pendulum is dependent only on length of pendulum. The gravitationalforce reduces slightly as we move to higher altitudes, and therefore the pendulum of samelength will have slightly longer period at higher altitudes.

A 248.7 mm long simple pendulum will have a period of one second at sea level. This periodwill double if the length is made four times, and triple if length is made nine times.

Factors Affecting the Time Period of a Simple Pendulum

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