Investigate the factors, which affect the time taken for one complete swing (time period) of a simple pendulum.

80

7.00

8.50

7.00

.70

70

5.92

5.60

5.76

.57

60

4.50

1.00

4.50

.45

50

2.40

3.00

2.50

.25

40

3.45

3.12

3.29

.32

30

0.36

0.37

0.44

.04

20

05.00

08.88

06.94

0.69

0

06.87

06.96

06.92

0.69

Red numbers are anomalous results

Blue numbers are estimated results

Analysis

From our results we can tell that the length of the string does affect the time for one swing. This graph has an obvious trend. The data points create a perfectly sloped line. This proves that length of the string indeed effects the period. Consequently, the longer the string is, the greater the period. A pendulum with any mass dropped from any angle would have the same period as a pendulum with a totally different mass and angle. In our results we encountered anomalous results, which meant we had to use estimated results instead of actual ones. This could have happened due to several reasons. The interaction between the clock and pendulum release could have been delayed or miss timed to cause an incorrect timing. Increased wind resistance may have slowed down the pendulum or an increase in force may have sped it up. As the pendulum was done near a wall increased friction may also have slowed it down. To make the estimated results we used the first timings. To make it a fairer and more accurate I would place the pendulum in the middle of a room free from obstructions so fairer results would be taken. I would also make sure there would be no draughts or wind that could air currents or increased friction. Also I would use a digital clock linked to a digital releasing system so both happen at the exactly same time and a computer could record the times for more accuracy. We only chose to study the length of string, as we knew it would be the only one that would affect the results. The mass of the bob and angle of release has no affect on the pendulum motion and timing.

Evaluation

Pendulum is a mass, called a bob, suspended from a fixed point so that it can swing in an arc determined by its momentum and the force of gravity. The length of a pendulum is the distance from the point of suspension to the centre of gravity of the bob. Chance observation of a swinging church lamp led Galileo to find that a pendulum made every swing in the same time, independent of the size of the arc. He used this discovery in measuring time in his astronomical studies. His experiments showed that the longer the pendulum, the longer is the time of its swing. Christiaan Huygens determined an exact relation between the length of the pendulum and the time of vibration when the arc of swing is small. Forces acting on the bob, such as air resistance, affect its swing. Since gravity varies from place to place, the pendulum has been used to determine the shape and mass of the earth by measuring the intensity of gravity. In 1851, J. B. L. Foucault demonstrated the rotation of the earth by suspending in the Panthéon in Paris a 200-ft pendulum that traced its path on the floor. The pendulum continued to vibrate in a single plane as the earth rotated underneath it, so it left a load of traces in the sand in all directions. Harmonic motion is regular vibration in which the acceleration of the vibrating object is directly proportional to the displacement of the object from its still position but oppositely directed. A single object vibrating in this manner is said to have simple harmonic motion (SHM). More complex harmonic motion can be analysed as combinations of two or more simple harmonic motions. An example of object which motion approximates SHM is a pendulum swinging in a small arc. Simple harmonic motion is a periodic motion; that is, it repeats itself at regular intervals. The time required for one complete vibration of the object is the period of the motion. The inverse of the period is the frequency, which is the number of vibrations per unit of time. The maximum displacement of the object from its central position of equilibrium is the amplitude of the motion. At maximum displacement the velocity of the object is zero; the velocity is greatest when the object passes through its equilibrium position. These terms are commonly used to describe any periodic phenomenon, e.g., wave motion and the rotation or revolution of an astronomical body. For any real harmonic motion, various forces act to reduce the amplitude with each vibration, i.e., to damp the motion. If these forces are small compared to the restoring force arising from the original displacement, then the object will vibrate a number of times with successively smaller amplitudes until the motion gradually dies out; this is known as damped harmonic motion. For a certain value of the damping forces, the object returns to its original position in a minimum amount of time and comes to rest at that position; such motion is termed critically damped. If the damping forces are large compared to the restoring force, the object returns slowly to its original position without vibrating at all; the system is said to be over damped.

Daniel Sibley