Example Calculation 1
Adding the uncertainties:
Therefore, the final value is:
21.7 cm ± 0.525 cm
Similarly, the calculations were performed for other readings
- An average of the time values(in s) for each reading was taken
- The calculation for the average time for string of length 20 cm is shown below:
Calculation 2
Averaging the uncertainties:
Therefore, our final answer stands as:
9.5 ± 0.5s
Rest of the calculations have been noted in the table below
Table 1.2 – Total Length and Average time for 10 oscillations
- We then convert the time period for 10 oscillations to the time period for just one oscillation
- An example calculation using unitary method for the 1st time period is shown below
Example Calculation 3
Similarly, calculations were performed for the other values of average time period and noted in the table below:
Table 1.3 – Total Length and Average time for 1 oscillation
Theory tells us that the calculation for the time period of a simple pendulum undergoing simple harmonic motion can be carried out by using a predefined formula:
T = 2
Where T(s) stands for time period, l(m) for length and g(ms-2) for the gravitational acceleration experienced by the object undergoing the motion.
T T2
OR, T2 = g = ; k being a constant.
So, to obtain a value for g, we must square the time period for each length, which would lead to the uncertainty being squared, and also convert the values of length to metres, which would also lead to the uncertainty being divided by 100:
Table 1.4
Conclusion
Aspect 1:
-
Theory states that the value of g=9.8ms-2 can be found by studying the relationship between length of the pendulum string and oscillations
- As we can see from this experiment the theory is correct but not completely.
- But, because the value of g obtained is not close to that of the theoretical value, we can assume that a variety of errors can be propagated in this experiment
Aspect 2:
- Random errors are introduced into this experiment by holding the pendulum bob at uneven and unequal extreme positions at the start, which lead to either higher or lower readings for the value of time period
- The ruler used could not be placed directly next to the string, and a rough estimate for the length of the string had to be taken, this leads to a higher or lower reading being taken for the value of length of the string
- Because the string was roughly tied around its support, the oscillations of the bob were haphazard and all over the place. These unnatural oscillations constitute a systematic error, and once again lead to either higher or lower readings for the value of time period
- Because the time period for one oscillation was too hard to measure, instead, the time period for 10 oscillations was taken. Multiple readings were taken, and averaged out to reduce error
- The base of the holder was uneven, and could lead to unnatural oscillations, which constitute a systematic error, and once again lead to either higher or lower readings for the value of time period
Aspect 3
- A proper apparatus with a rigid support to suspend the string, along with an attached tape measure would reduce the random and systematic errors in this experiment
- More number of readings could be taken, and averaging them would negate most of the random errors in this experiment
by
satishahuja95 (student)
