Simple Harmonic Motion Report

Abstract

The aim of the laboratory assignment is to learn the properties of oscillation via performing the experiments and calculations. The oscillation parameters are important since the phenomenon is widely applied in industry, and there are numerous natural phenomena that involve oscillation.
During the experiment, the time and amplitude of oscillation were measured. The experiment was conducted in several replicates to ensure the accuracy.
Basing on the experiments, the oscillations, natural frequency and damping have been estimated. The experiments allowed understanding the oscillation and damping phenomenon, and the knowledge was strengthened by calculations.

Introduction 4

Experimental 4
Results and Discussion 4
Conclusions 7

Reference List 8

Introduction
Oscillation is a common phenomenon for nature and industry. The oscillations of grass and trees are observed at the wind. At the sea storm, the waves are water oscillations. The heart beat is an oscillation. Numerous technical, social and areas, as well as thermodynamical systems are influenced by oscillations and dumping. Oscillation is a vibration around the equilibrium point that repeats in time (King 2009). Since the phenomenon is common in every field of activity, understanding of the phenomenon and its characteristics is an important for every educated person.
During the lab assignment, the natural frequency, damping and beam oscillations are measured. The repeated measurements are performed to ensure quality and correctness. The basic oscillation characteristics, namely frequency and damping are computed by theoretical formulae.
Experimental
The experiment was performed with a specific device that is illustrated in Figure 1. There are the following compartments: spring (1), beam (2), dashpot (3), paper drum (4).
Figure 1: The experimental device for oscillation measurement
The beam oscillations are studied. One of the beam ends is attached, and the other is free. There is a spring (1) connected to the beam free end. The item that oscillates is a cylinder 3 filled with oil; it has a piston. The data are recorded by a paper drum (4), rotated by a paper with a constant speed. The beam is equipped with a pen. There is a control unit that regulates the turning speed of the chart recorder. The paper taut is kept with weights. The stopwatch is used for time measurement, and a ruler is required to measure the amplitude. The accuracy and systematic errors are managed by the repeated measurements, which are realized as three replicates (Ross & Lawrence 2013).
Results and Discussion
Speed of the paper is depicted on Graph 1. The length of the line is 39.42 mm.
Graph 1: The paper drum speed measurement.
The line is graphed in 2.91 seconds. The speed of the paper calculates as:
υ=length(mm)time(s)=39.422.91=13.54 mm/s.
The time of the oscillation is calculated as:
Ts=L(mm)υ(mms),
where L stands for the distance between the two peaks. The graphical representation of the results of the distance measurements between the two successive peaks are on Graphs 2.1-2.3 (for replicates 1-3, respectively).
The experiments with with the dashpot and fully and partially opened holes are presented in Graph 3.1-3, Graph 3.3-6, respectively (replicates 1-3).
Graph 3.1
Graph 3.2
Graph 3.3
Graph 3.4
Graph 3.5
Graph 3.6
The experimental measurements are summarized in Table 1. The calculations are also performed.
The average rate of the beam loss is approximately 45%, the system damping without dashpot calculates as:
δ=lnA0A0-0.45A0=ln17.6417.64-0.45∙17.64=0.59.
The replicate measurements were involved to handle the experimental error and to avoid the systematic error (Ross & Lawrence, 2013). Basing on this strategy, the natural frequency of the beam oscillations was assessed. The damping phenomenon was calculated.
Although the repeated measurements were performed, the experimental methodology has several drawbacks. Namely, it is limited by human sight and reaction. The accuracy might be improved by application of the automatic measurements devices,
As the dashpot was added, the frequency reduced, since the conditions of the oscillations reduced.
Conclusions
The laboratory experiment was mentioned to gain knowledge on basic parameters of the simple harmonic oscillation: period, frequency, and damping. The studied values were repeatedly measured on the experimental set up, and the results were processed with calculations. Using the experimental data, the frequency and damping were calculated by theoretical formulae.
Reference List
King, GC, 2009, Vibrations and waves. Chichester, U.K., Wiley.
Ross, D, & Lawrence, DA, 2013, Master math. Master everything from motion, force, heat and work to energy, fluids, waves, optics and electricity. Boston, MA, Course Technology PTR.