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Unformatted text preview: Simple Measurements Simple Pendulum & 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 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 = *diameter) and the value of 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 obtained as a result of our experiment. We can then determine how far our experimental results of deviate from the actual value of 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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This note was uploaded on 01/09/2012 for the course ELECTRICAL 1221 taught by Professor Tan during the Spring '11 term at National University of Singapore.
- Spring '11