• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

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.

...read more.

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.

image00.png

image01.png

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.

image02.png

image03.png

image04.png

image05.png

length

image06.png

√Time

...read more.

Conclusion

The following formula can be derived from these principles;-

image07.png

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:

image07.png

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

...read more.

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

See related essaysSee related essays

Related GCSE Forces and Motion essays

  1. Period of Oscillation of a Simple Pendulum

    When the mass was altered in my experiments, the size of the object changed along with its aerodynamics. This therefore theoretically slowed the object down. But, in my results, this is not shown because if air resistance was a big factor, then the results at the beginning would be quicker.

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

    Record the time. 13. Adjust the length of the pendulum for the next reading. Remember to measure the length of the string from the middle of the bob to the edge of the wooden blocks where the string comes out.

  1. 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.

  2. Strength of a string practical investigation

    Load (kg) Test 1 Test 2 Test 3 Average extension (m) Force (F=ma) Stress (F/A) Strain (E/L) 0.5 0.001 0.001 0.001 1.00E-03 4.9 1.93E+06 1.54E-03 1 0.001 0.001 0.001 1.00E-03 9.8 3.86E+06 1.54E-03 1.5 0.001 0.001 0.001 1.00E-03 14.7 5.79E+06 1.54E-03 2 0.001 0.002 0.001 1.33E-03 19.6 7.72E+06 2.05E-03 2.5 0.002 0.002

  1. Prove that "Frictional Forces are Surface dependant".

    I will observe the block fly across the surface, and I will have my finger on the stop button in the watch, and that's to stop it once the block reaches the end of the surface, or if it stops in the middle of the surface.

  2. Damped Oscillation.

    In my assumption I said that the resistance was proportional to velocity. So. In this case velocity is , hence . My first model of this situation is completed. The model is as follows: * Manipulating the model I am going to solve this differential equation.

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