Investigating a factor which can affect the period of a pendulum.

From where I found this explanation , I also found a mathematical equation relating the length of a pendulum to the time taken for an oscillation, stating that:

T=2? V l

g T= Period/time taken for 1 oscillation

l= Length of thread of pendulum

g= Gravitational field strength= 9.8N/kg

This formula can be simplified by squaring both sides to give:

T²= 4?² l

g

As 4, ?, and g are all constants, l is the only variable that is changed and so, T is affected by l being altered. Therefore T² must be directly proportional to l.

I can now state that the length of the pendulum does have an effect on the time for 1 oscillation and that as the length of the pendulum increases, so does the period.

I will draw a graph of T² against l; if the line is straight with a positive gradient and going through the origin, it will support my statement that T² is directly proportional to l.

Method:

-Set up a clamp stand, clamped to a table by the use of a G-clamp.

-Attach a piece of string 1.5 metres long to it, using a third of that length (0.5m) in knots etc...and remembering to knot a loop for the bob to be hung, finishing in 0.8 metres of string hanging vertically from the clamp.

-The variable of length will be altered for the experiment using a meter ruler.

-A bob of weight 500g is attached securely to the end of the string's loop.

-The pendulum will be drawn back to an angle of 30° (measured with a protractor) and then released.

-The stop clock will be started, 10 oscillations counted and at the end of the 10th oscillation, the clock stopped.

-For each different length of the pendulum, the experiment will be repeated 3 times, in order to obtain an average.

-After each length, the string will be lengthened by 10cm.

-All results will be recorded and from them, a graph plotted.

We will take 8 reading, each with an interval of 10 cm between them, starting with 0.1 metres to 0.8 metres.

Precise uses of measurement will be used to ensure that the variables change/remaine constant during the experiment:

-Using a metre ruler to measure the pendulum's length.

-Using a protractor to measure the pendulum's angle of altitude

-Using a stop clock to measure the pendulum's period(s) to 2 decimal places of a second.

-Using 5 x 100g masses to measure the pendulum's bob of 500g.

Not many safety risks were involved, although the following should be considered to provide a safe test:

-The angle of altitude was kept to a minimum of 30° to avoid large swings leading the bob to come into contact with anything and causing damage.

Preliminary work:

We researched our investigation before carrying out the experiment by looking at theories and equations in A level Physics text books. We also carried out a very short experiment with a pendulum of length 20cm and of 50cm to see if there was a big enough difference to get varied results for the more detailed experiment.

Fair test:

To ensure accurate and reliable results, the following will be considered:

-So that the velocity of the swing is not affected, we will make sure that there are no obstructions to the swing of the pendulum.

-The interval between the string's length will increase by only 10cm each time; this will help prove a clear pattern in the results.

-The angle of altitude will remain as 30° throughout, ensuring there is no change in the forces acting upon the pendulum.

-The mass of the pendulum (bob) will remain the at 500g throughout, ensuring there is no changes in the forces acting upon the pendulum.

-The clamp stand will be securely fixed by the device of a G-clamp so that it doesn't move, affecting the results.

Apparatus needed:

Clamp stand, G-clamp, string, metre ruler, protractor, stop clock, 5 x 100g weights

How the apparatus will be set up is shown below:

OBTAINING EVIDENCE

I followed the method in my plan, taking 3 readings for each length and measuring the time taken for 10 oscillations and then dividing this number by 10 to obtain the average time for 1 oscillation. All of these results were recorded in a table (see next page) as well as the results for the predicted time from using the formula shown below.

Pi

T²= 4?² l length of pendulum (variable)

g (referring to mass of bob) gravitational pull = 9.8N per kg

Time for 1 oscillation (period)

E.g.: In the case of the length of the pendulum being 0.1 metres (10cm).

T²= 4?² l

g

= 4 x ?² x 0.1

9.8 x 0.5 we used a bob of mass 500g=1/2 kg

= 39.48 x 0.1

4.9

= 8.06 x 0.1

= 0.806

T = V0.806

= 0.90 seconds

ANALYSIS & CONCLUSION

Graphs found on previous pages

Conclusion:

The graphs clearly show smooth curves with positive gradients which signify that the period increases as the pendulum's length increases.

EVALUATING

Accuracy of results:

The results obtained from applying the formula were accurate through the use of a calculator. However the results obtained from the experiment were not accurate as they did not match those of the formula. The lines on the graph show that both sets of results follow the same pattern but with a large difference between them, on average, 3.1 seconds due to a systematic error that should have been corrected.

There was one anomalous result obtained through the experiment, this was the last reading of the experiment at the length of the pendulum being 0.8m. When plotted on the graph, the last result does not have as big a difference with the previous result than that of all other results.

These inaccurate results and one anomalous result acquired in the experiment are, most likely, due to human error. Factors which may have affected the accuracy of the results include:

-Error in measuring the length of the pendulum. This was due to 2 different persons reading the length of a metre ruler and interpreting unlike readings. To improve the accuracy of the pendulum's length, 1 person could be in charge of measuring the length and mark the length on the string with a pen.

-Error in measuring the pendulum's angle of altitude. This was due to 2 different persons reading the angle on a protractor and interpreting unlike readings. The 30° angle proved difficult to measure and it was hard to get the pendulum at the exact angle for each different length. To improve the accuracy of the reading of the pendulum's angle of altitude, 1 person could be in charge of reading the protractor and attach the protractor to a clamp stand so that it was in a fixed/straight position to take readings.

-Human reaction time. Human reaction time could have led to the measured period time being judged inaccurately. This is due to slow reactions when operating the stop clock etc. To improve human reaction time, the experiment could have benefited from the aid of a scientifically based computer with sensor or camera which may have been able to record the energy of the oscillations and watch and time the pendulum, displaying results as it calculated them.

Excluding human error, the procedure and formula exercised were regarded as reliable and so, I can support that my evidence concludes that one factor that affects the period of a simple pendulum is its length. When the length increases, the period increases; when the length decreases, the period decreases.

The procedure and formula exercised was understandable and straightforward; however certain improvements could be made to make results more efficient by being more reliable. More repeats could have been applied to the method to obtain a more specific average. The pendulum's length was in the form of string, as a result of having 500g suspended on it, the string could have accumulated extra length by being stretched; this could have been improved by using stronger, more rigid material as the pendulum's length. When measuring the length of a pendulum, instead of guessing where the end of the bob is against the metre ruler, the ruler could have been placed level with the point of suspension and a set square placed along it, touching the bottom of the pendulum to improve accurate readings.

To extend this investigation, I would further explore the relationship between mass and/or angle of altitude and a pendulum's period. Also, how the pendulum differs when its factors are affected by a different gravitational field strength, not 9.8 Newtons per kg.

All these different relationships would help provide a deeper understanding of factors that affect a pendulum and so, I would be able to provide additional evidence to support my conclusion and scientific theory.