• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month
Page
1. 1
1
2. 2
2
3. 3
3
4. 4
4
5. 5
5
6. 6
6
7. 7
7

# The Pendulum

Extracts from this document...

Introduction

Maths II Project:

The Pendulum

The following report was prepared for the Pure Maths II topic of Models of Growth. This report aims to investigate the relationship that may connect the period of a pendulum with it’s length.

A pendulum is a body suspended from a fixed point so that it swings back and forth under the influence of gravity. A simple pendulum consists of a weight suspended at the end of a string. The periodic motion of a pendulum is constant, but can be made longer or shorter by increasing or decreasing the length of the string.

To investigate the period of a pendulum, we began by constructing a simple pendulum (see appendices 1). To measure the time for one complete oscillation (the back and forth ‘swinging’ motion), we decided to time eight complete oscillations.

Middle

15.25

15.26

1.91

100

16.07

16.01

16.13

16.07

2.01

* Time taken after 8 oscillations.

We decided to measure eight oscillations and then find an average per oscillation as this is more accurate. If only one oscillation was used, then the person’s reaction time to stop the stop watch would probably be greater than the time of the oscillation.

The average time per oscillation was found by dividing the average of the eight oscillations by eight.

The graph of Time Vs Length can then be plotted to try and establish the rule connecting the period of the pendulum with it’s length.

From this graph there appears to be a logarithmic or power relationship between the period (T secs) and length (L cm). To investigate this, graphs using:

• T Vs Log L
• Log T Vs Log L
• Log T Vs Log L
• T Vs L
• T Vs L

can be plotted to determine the relationship connecting L and T.

length

√Time

Conclusion

The following formula can be derived from these principles;-

At a given place on earth, where g is constant, the formula shows that the oscillation period T depends only on the length, L, of the pendulum. Furthermore, the period remains constant even when the amplitude (the angle) of the oscillation diminishes due to losses in energy such as the resistance of the air,

This property is what makes pendulums good time keepers as they inevitably lose energy due to frictional forces, their amplitude decreases, but the period remains constant.

In conclusion, I found that Time is proportional to Length and hence found the relationship between L and T to be:

T = 0.2087L – 0.0639

This relationship also supports the formula for calculating the period of a pendulum:

While researching the relationship between the period, length and mass of a pendulum, I found these web sites useful.

http://theory.uwinnipeg.ca/physics/shm/node5.html

http://www.gmi.edu/~drussell/Demos/Pendulum/Pendula.html

http://www.picotech.com/experiments/pendulum/pendulum.html#discussion

http://www.tmeg.com/esp/p_pendulum/pendulum.htm

This student written piece of work is one of many that can be found in our GCSE Forces and Motion section.

## Found what you're looking for?

• Start learning 29% faster today
• 150,000+ documents available
• Just £6.99 a month

Not the one? Search for your essay title...
• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

# Related GCSE Forces and Motion essays

1. ## Period of Oscillation of a Simple Pendulum

However, when I observed the angle of release experiment, I noticed that after about 45�, the pendulum appeared to 'flop'. I believe this was due to the speed needed to keep the pendulum string taught. Enough speed is needed to keep the string from 'bending.'

2. ## The determination of the acceleration due to gravity at the surface of the earth, ...

Release the pendulum, so it starts swinging. Make sure it is swinging in one plane, so from right to left and not on more than one plane, perhaps in circles. If it is, stop the pendulum and do this again. You will need to make sure that when you measure the 10?

1. ## Determining the acceleration due to gravity by using simple pendulum.

Rather, he used measurements based on pendulums. It is easy to show that the distance a body falls is proportional to the time it has fallen squared. The proportionality constant is the gravitational acceleration, g. therefore, by measuring distances and times as a body falls, it is possible to estimate the gravitational acceleration.

2. ## Physics Coursework: To investigate the Oscillations of a mass on a spring

Therefore, for bigger masses or longer springs, the accelerations will be smaller and thus the velocity is also smaller. It will take a longer time to complete the same oscillation. I also believe the maximum velocity will be in the centre of the oscillation.

1. ## In this Coursework, we were given the task of investigating some factors which affect ...

suspended object has to travel further than that of a smaller angle, its higher velocity compensates for it & visa versa. I therefore think that the advantage of the smaller angle having a smaller distance and having a smaller period is cancelled out by the increase in Kinetic Energy leading to greater velocity, found in larger angles.

2. ## Strength of a string practical investigation

will get three sets of results for each string and then average the results to give me more reliable results (This will filter out any extreme values gained from experiments). I will follow the fair test requirements and safety procedures throughout the experiment so to keep all results reliable.

1. ## Damped Oscillation.

We are able to find out the value of . The diagram below shows a simple pendulum motion. The acceleration in the transverse direction is given by. Applying Newton's second law in the transverse direction gives . Dividing both sides by m and using the small angle approximation, the equation of motion is .

2. ## Prove that &amp;quot;Frictional Forces are Surface dependant&amp;quot;.

The coefficient of static friction between rubber and asphalt is 0.60, and the acceleration due to gravity, g, can be taken to be 10?m?s?2. Solution The car resists any attempt to move it due to its weight, which is equal to its mass multiplied by the gravitational acceleration g.

• Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to