Simple Measurements – Simple Pendulum &
π
Estimation
Wang Zhikai
Group A1
Pc1221 Lab Report: Simple measurements
1
Objective
Demonstrate the specific knowledge gained by repeated physical measurements.
Apply the statistical concepts of mean, standard deviation from the mean and standard error to
these measurements.
Demonstrate propagation of uncertainties by determining the uncertainty in the calculated
quantities from the measured quantities.
Demonstrate the method of linear least square fit by determining a value of the mathematical
constant
π
from measured diameters and circumferences of circles.
2
Introduction
A simple pendulum is an assumption of ideal conditions to produce a situation where,
provided the angle of release is small, the period of the pendulum stays constant. The
pendulum is kept moving by gravity and oscillates about its equilibrium position. However,
pendulums in the real world do not function under ideal conditions and are affected by
friction and air drag.
The purpose of this experiment is to obtain the different readings produced by measuring
the same pendulum multiple times. We can then determine how far our experimental results
deviate from the results predicted by the theoretical relationship between the period and
length of a simple pendulum. We will then be able to analyse the factors that caused the
deviation.
The circumference of a circle and its diameter are related by the formula (circumference =
π
*diameter) and the value of
π
has more or less been decided to be 3.14159265 in value.
The purpose of this experiment is to obtain the different readings produced by measuring
the multiple circles’ circumferences and diameters multiple times. We can then use the
formula linking the two dimensions to calculate the value of
π
obtained as a result of our
experiment. We can then determine how far our experimental results of
π
deviate from the
actual value of
π
which has been accepted to be the accurate value worldwide. We will then
be able to analyse the factors that caused the deviation.
3
Methodology
Part A: Simple Pendulum
1)
We used a digital balance to take 10
independent measurements of the mass and weight of the
ball bearing of the pendulum. The digital balance was first tared with nothing on the balance
pan to ensure the readings taken were as accurate as possible.
2)
We then measured the length of the simple measurement using a measuring tape 10
separate
times to obtain a sample of the variation in the length of the simple pendulum. We did not line
up either edge of the simple pendulum with the end of our measuring tape; instead, we took
two readings of the start and end of the pendulum and used these two readings to calculate a
more accurate measurement of the pendulum.
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 Spring '11
 Tan
 Ball bearing

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