FACTORS AFECTING SIMPLE PENDULUM`S PERIOD

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Name: ashkan mohseni hosseini                               Consultant teacher: Mr. McCormack

Period of Oscillation of a Simple Pendulum

Aim: to consider the time taken for a pendulum released from angle until it gets back to the point where it was released i.e. period and hence the effective factors such as : mass, angle, gravity ,viscosity and length. So I will consider each separately.

Hypothesis: in physics we have a formula called Galileo’s formula stating:

                                                     T = 2Π√(l÷g)

In which l is the length of wire and g is the gravity and indicates to what factors period depends on. Actually this rule says that the longer the thread is the higher the period is and vice versa.

Purpose of pilot work: now I am going to practically investigate to see whether I can prove the Galileo’s formula experimentally by considering the change in period by changing other factors.

Description of pilot work:  I am thinking of designing an apparatus consisting of an object mounted so that it swings freely under the influence of gravity. So the first things that their need come to mind are: sphere shapes as our pendulum, a inflexible string whose weight is negligible, clamps and retort stand, a crocodile clamp and ruler and stop clock.  

And here is how I designed my apparatus:

First I put a stand on a table then I secured a clamp at the top of the rod to tie up desired length of the thread which has the pendulum attached to its bottom to the clamp. Then I put another clamp on the rod just under the first clamp and I attached a protractor to it so that I can measure the angle of swing .And my variable was length and so I used different length of thread and for each length I repeated the experiment so many times until I got three consistent results for each length.

Safety: There are no safety precautions that need to be taken into considration in this experiment, only common sense should be observed).

Length: as we can see from the equation the length is one of the effective factors on the period of the pendulum so I measured the thread for different lengths. As the Galileo’s formula says mass of pendulum and the angle from which the pendulum is released do not effect the period but I haven’t proved them yet so I keep every variable apart from length unchanged and angle I will choose is 10° and the mass of pendulum is 0.05 kg. I will do some further experiment to make sure that those effect mentioned don’t have any effect in the period).

 And here are the results I got:

How I got those values in the last column: as we know the length of the thread and the gravity I can use the equation T = 2Π√(l÷g). For example for the 10 cm long thread I can find the period as follows: T= 2×Π×√(0.1 ÷ 9.8) =0.635

  • I did not have to change my experiment as I found it work well but there are some slight problems with my results in the length of 10cm and 55cm and order to explain them I need to introduce some new terms.

Accuracy:  is defined as the ability of a measurement to match the actual value of the quantity being measured". If in reality it is 34.0 F outside and a temperature sensor reads 34.0 F, then than sensor is accurate.

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Precision: could be divided into two major part: 1) resolution 2) sensitivity

(1) (Resolution): The ability of a measurement to be consistently reproduced

(2) (Sensitivity):  the number of significant digits to which a value has been reliably measured. If on several tests the temperature sensor matches the actual temperature while the actual temperature is held constant, then the temperature sensor is precise. By the second definition, the number 3.1415 is more precise than the number 3.14.

Look at the examples below:

        

  • Examples from my results contain the results for 10cm length in which as we ...

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