Example Of Report On Simple Harmonic Motion

Abstract

The laboratory aims to study the basic characteristics of oscillation that are required for various industrial and research tasks. The specific experimental set up has been used. The following values have been measured experimentally: time and amplitude. Although these variables are easy to calculate, they provide the sufficient information about the studied subject.
The natural frequency, damping and oscillations of a beam have been calculated. The oscillation experiments are conducted and the calculations are performed. The measurements are simple and do not require the specific devices. The damping is explored and calculated. The applicability of the experimental method is assessed.

Introduction 4

Procedure 4
Results 5
Discussion 8
Conclusions 8

Reference List 9

Introduction
Every person is familiar with movement as it is a part of our everyday life. Oscillatory motion refers to repeated back and forth movement over the same path. There are simple examples of oscillatory movement, e.g. the movement of a walking person's arms, bird's wings at flight, swaying the tree leaves. The piano or guitar string oscillate to produce sound. Oscillation is characteristic for molecules and atoms, as well as for complex man-made systems (houses and various devices). All types of the waves oscillate, namely raio-, micro-, acoustic-, and electrical waves (Fitzpatrick 2013). Therefore, the studies of oscillation and its characteristics is an important practical task.
The simple harmonic motion refers to oscillation with one degree of freedom, or the one that is able to oscillate only in one direction. The simple harmonic motion has three basic characteristics. These are amplitude, time period and frequency. Amplitude is a maximum or minimum displacement of the item from the mean (zero) position. Period is an interval which is required for the oscillation to repeat. For convenience, the number of oscillations per interval (reciprocal period) is called frequency. Damping is the eventual extinction of oscillations, which results in decay of the amplitude. Damping appears due to energy loss (Fitzpatrick 2013).
The aim of the experiment is measuring the natural frequency, damping and oscillations of a beam. To achieve this, a beam was oscillated. The frequency and damping are calculated from period of oscillations and amplitudes.
Procedure
Figure 1 depicts the experimental set-up.
Figure 1: The test set-up. 1 – spring; 2 – beam; 3 – dashpot; 4 – paper drum.
The rectangular beam 2 is clamped on one end and free on the other. Spring 1 is attached to the free end of the beam. A cylinder 3 filled with oil with a piston is attached closely to the fixed end of a beam. A paper drum 4 acts as a chart recorder. It is a slowly rotating drum with a paper roll that moves at constant speed. A pen is attached to the end of the beam 2. The system is controlled by a control unit that controls the turning speed of the chart recorder.
The small weights are used to keep the paper taut; the measurements require a stopwatch and a ruler (Fitzpatrick 2013). The experimental errors are minimized by the repeated measurements; three replicates are made for each experiment (Newman 2008)
Results
1. Graph 1 illustrates the length of the straight line drawn in 2.91 seconds.
Graph 1: The line for calculation of the paper drum speed
The speed of paper is:
υ=length(mm)time(s)=39.422.91=13.55mm/s.
2. The time of the oscillation is calculated as:
Ts=L(mm)υ(mms),
where L is the distance between the two successive peaks. The experimental results are presented on Graphs 2.1-2.3 (for replicate readings).
Graph 2.1: The distance between the two successive peaks (reading 1)
Graph 2.2: The distance between the two successive peaks (reading 2)
Graph 2.3: The distance between the two successive peaks (reading 3)
Graph 3.1: The distance between the two successive peaks with the dashpot and fully opened holes (reading 1)
Graph 3.2: The distance between the two successive peaks with the dashpot and fully opened holes (reading 2)
Graph 3.3: The distance between the two successive peaks with the dashpot and fully opened holes (reading 3)
Graph 3.4: The distance between the two successive peaks with the dashpot and partially opened holes (reading 1)
Graph 3.5: The distance between the two successive peaks with the dashpot and partially opened holes (reading 2)
Graph 3.6: The distance between the two successive peaks with the dashpot and partially opened holes (reading 3)
The measurements results are presented in Table 1.
Taking into account that the beam loses about 40% of its amplitude at each oscillation, then the damping of the system without dashpot estimates as:
δ=lnA0A0-0.4A0=ln0.2140.214-0.4∙0.214=0.49.
Discussion
The experimental setup allows measuring the natural frequency of the beam oscillations. The tests were performed as three replicates for each experiment to minimize the experimental errors and exclude the systematic errors (Newman 2008).
The oscillation period and frequency were determined. The damping for oscillations with a dashpot was calculated basing on the experimental results.
The results accuracy is limited by the length and stopwatch measurements, as well as by the reaction and attention of the experimenter to observe the oscillations. The improvements of the test are about improvement experimenter’s skills and attention (Breithaupt 2010).
The natural frequency changes as the damping is added. Actually, the natural frequency refers to frequency without damping (Kumar 2005).
Conclusions
The laboratory assignment aimed to study the oscillation and its characteristics: period, frequency, and damping. The values were measured experimentally with the replicates procedure, the results were processed and calculated. The period and frequency of oscillations were determined, and the damping was assessed.
Reference List
Newman, J, 2008, Physics of the life sciences. New York, Springer.
Breithaupt, J 2010, Physics. Basingstoke [England], Palgrave Macmillan.
Fitzpatrick, R 2013, Oscillations and waves: an introduction. Boca Raton, FL, Taylor & Francis.
Kumar N, 2005, Comprehensive physics for engineers, Laxmi Publs.