Experiment of Simple Pendulum( Add Math Project Answer )

Aim: To investigate how the length of the simple pendulum affects the time for a complete swing.

Inference: The length of a pendulum affects the time taken for 20 complete oscillations.

Hypothesis: The longer the length of the pendulum, the longer the period for 20 complete oscillation.

Variables: Manipulated : The length of pendulum, 1

Responding : The period, T for a complete oscillation.

Constant : Mass of pendulum.

Material & Apparatus: a string of 5 cm till 60 cm of length , a retort stand with clamp, a pendulum bob , a protector,ruler, and a stop watch.

Procedure :

1. A simple pendulum was set up by attaching an object to a string of length of 60 cm.

2. The pendulum was set in motion and the time taken was measured (t/s) for 20 complete oscillations.

3. The period, T/s, that is the time taken for one complete oscillation was calculated.

4. Step 1-3 was repeated using at least 10 different lengths of strings with the minimum length of 5 cm.

5. The reading was recorded in a suitable table.

6. A graph of period, T(s) against length, l (cm) was plotted, the graph plotted was interpreted.

Result :

Values obtain from this experiment:

6)Plot a graph of period ( T s ) against length ( l cam )

Comment on the graph obtained..

7(a)Suggest at least two different pairs of variables for the horizontal and vertical axes to obtain a linear relation.For each pair,plot the graphs and draw lines of best fit manually and by using ICT

The relationship between the period and the length is

The gravitational acceleration g is constant (not variable). Therefore the variable is T and ?l.
If we square both sides of the equation, it become

Hence the 2 variables are T² and l.

The 2 pairs of variables are:

1. T and ?l (T as verticle axis and ?l as horizontal axis)

2. T² and l (T²as verticle axis and l horizontal axis.)

7(b). Estimate the gradient of each graph.Hence,write an equation relating period and length for each of the graphs.

7(c). Use the gradient of each graph to determine the respective value of the gravitational acceleration,g ms-2.Comment on the values obtained.

How do these values of g compare with the accepted value of g on earth(9.807 g ms-

Calculate the percentage error for each of the value of g obtained.
Explained the difference(if any).

Comment
This value is slightly lower than the accepted value 9.807 ms^-2.

Percentage of Error

The y-axis = T²
The x-axis =l, hence
The gradient = 4?²/g

From the graph, we know that the gradient is equal to 0.038 . Therefore

Explanation the Differences
Both of the values that we got is slightly lower than the accepted value. This is most probably due to the presence of air resistance. This error can be reduced by reducing the angle of oscillation.

Another possible source of error is the pendulum did not oscillate in a plane but in circle. This make the pendulum become a cone pendulum, where the calculation will be different from a simple pendulum.

7(d) Use the graph with the least percentage error in g to determine the length of string that will produce a complete oscillation in 1 second.

The graph with the least percentage error is the graph of T against ?l, the relationship between the period and the length is

A simple pendulum can be used as a device to measure time.Describe how you can use it to measure your pulse rate.

1. Make a simple pendulum of length 24.75cm (So that 1 oscillation is equivalent to 1 second).

2. Get a friend to count the number of oscillations for you.

3. Ask him to give instruction when should you start and stop (after 30 oscillation).

4. Start counting your pulse when your friend says start and stop counting after 30 oscillation.

5. Repeat this process for 3 times to get the average value, P_ave.
The pulse rate = the P_ave x 2.

9) If the length of the string is 4 times its original length,state the change in the period,Ts

Conclusion:
If the length of the pendulum increases by 4 times, the period, T will increase by 2 times.

Further Exploration
1) If a simple pendulum with a period of 1 second is set in motion on the moon,determine the new period of this pendulum.

OR

2 (a) Investigate whether a simple pendulum will swing continuously in air.Explain your findings.
Suggest the conditions required for a pendulum to swing continuously.

Explanation

Pendulum cannot swing continuously because there are external friction ( air etc ) unless doing the experiment in vacuum. ( an analytical prove is necessary )

2.(b) If a pendulum is made to swing in water,compare the time taken for this pendulum to come to a complete stop with the time taken by a pendulum swinging in air.Explain the difference.

Explanation

(b) time taken for this pendulum to come to a complete stop in water will be shorter than swinging in air because water buoyant force & water resistance are greater than air friction. (an analytical prove is necessary)

3) Sketch graphs on the same scale to illustrate the motion of a simple pendulum swinging
1. in air,
2. in water and
3. in vacuum.

OR

My conclusion,

The practical result that I did, is actually has little different with the pendulum theory. This is mostly due to the mistake problem when I doing the experiment. For example, when I am recording the time for 20 oscillation, ts, I am recorded the slightly faster or slower value compared with the real vale. Besides, this also because when I swinging the pendulum,the pendulum is not perfectly plane horizontally, it may be swing as cone formed.

During this experiment, I have learnt the theory of the pendulum. I learned the differences of the pendulum swinging in different condition, and also the motion in moon. In this project, I find out the way of how to use the period of pendulum to calculate the pulse rate or the time. Lastly, i knew that a lot of the mathematics formulae and calculation is actually useful in our life.

This project work let my knowledge increased quite a lot. During this project work, I have learnt the history of the pendulum. For example, Galileo Galilei created the pendulum and Christian Huygens continued Galileo’s work and made the first pendulum clock, regulated by a mechanism with a “natural” period of oscillation.

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