Analysis
Part I
The dominant source of error in this
experiment is human error, which came across when we measured the time period
using a stopwatch. It should be noticed that the reaction time of an observer
is of great significance, as if it is not appropriate, then some errors will
likely to occur. The only way to minimize this error is by repeating the
experiment multiple times or by taking the average of up to ten trials.
A random error is a statistical fluctuation
in the measured data because of the precision limit of the measurement device.
On the other hand, a systematic error occurs because of a problem that persists
throughout the experiment. In this particular lab experiment, the systematic
error is lesser than the random error because it was the result of equipment
that was not correctly calibrated.
The formula used to determine the mean is
<x> = ∑x/N.
Here
∑ represents the summation
N represents the total number of scores
x represents scores
In order to calculate the random error, the
sum of all measurements has to be taken. Then it needs to be divided by N in
order to obtain the mean or average. Now, the value of mean can be subtracted
from the N measurements for obtaining N deviations. In the next step, the
square of these N deviations should be taken.
The error in the measurement is 4 percent.
Part II
The experiment was started with a 15° angle
from the vertical. Then it was repeated for 30°and 80° angles from the
vertical.
The value for the error in 10T is 0.7%.
In order to propagate the error to T, one has
to take individual mathematical operations into account, such as
multiplication, raising the number to power and addition.
Part III
The length of the pendulum was set to 50cm,
and then the experiment was repeated by increasing lengths by 1m in increments
of about 10cm.
Executive Summary
The major source of uncertainty is human
(errors) which come across when we measure the time period with the help of a
stopwatch. The second source of uncertainty is instrumental (errors) which we
have to face while using a digital stopwatch. The only way to avoid this
problem is by using an analog stopwatch rather than a digital stopwatch. The
arc angle can also cause uncertainty or error. In order to avoid it, we should
take small angles. Ideally, the angle of the arc should not exceed 30 angular
degrees. In addition, the friction between the swinging bob and the surrounding
air is a big source of uncertainty. We can minimize it by using a heavy bob
whose shape has to be spherical. Meter sticks or rulers should not be used, as
these can make it difficult for us to measure the length of the pendulum.
The time period is the time needed to
complete one cycle. It is symbolized with the capital letter T. On the other
hand, the amplitude is the measurement of energy that is transported from one
thing or component to another thing or component. The symbol for amplitude is
the capital letter A. Both the time period and amplitude are related to one
another as we always have to record the time when the energy is being
transported. There is a strong relationship between the length of a pendulum
and the time period. We can also say that the time period is independent of the
oscillation but is dependent on the length of the pendulum.
