Analysis Paper Lab Report and Discussion on the Results - 2750 Words

Analysis Paper: Lab Report and Discussion on the Results (Lab Report Sample) Content: Graphical analysisStudents nameInstitutional AffiliationGRAPHING AND GRAPHICAL ANALYSISObjectivesThe major objectives of this experiment are: 1 To understand graphs and graphical relationships. 2 To understand the use of error bars on graphs. 3 To recognize linear relationships, power relationships, and exponential relationships from the shape of the respective curves and to plot and determine the equations of such curves.Introduction and TheoryMany experiments are of the type where one wishes to discover the relationship between a pair of quantities that depend on each other, either to verify a theoretical prediction or to help guide the development of a theory where none exists. Examples of related pairs of quantities are: the velocity vs. time of a mass falling in a gravitational field, the period of oscillation vs. mass for a mass-spring system undergoing simple harmonic motion, and the specific heat of a substance vs. its temperature (Tukey J. 1977). 1 Functiona l RelationshipThere are many kinds of possible relationshipsy=f(x), but we will be concerned here with only three types: * Linear RelationshipA relationship is linear when the independent variable,x, is related to dependent variable,y, in the form y=ax+bWhere a and b are constants. * Power RelationshipHere the independent variable is related to the dependent variable asy=bxa * Exponential RelationshipsHere the independent variable is related to the dependent variable asy=beaxIn order to determine the appropriate relationship, one can refer to theory when possible, or construct a graph and proceed by trial and error. In the second case, one simply graphs y vs. x in excel. If the two quantities are related linearly, a straight line is obtained; otherwise, a curved line results, its general shape and position with respect to the axes can point to the appropriate relationship.II. Error Bars-part IError bars are graphical representations of the uncertainties in the data you are plotting. They facilitate the choice of which particular type of function best describes the relationship between the variables you are plotting. This is particularly true for linear functions. In order for the function to describe your data relationship correctly the curve must pass through most of the error bars (Peakall et al, 2006). 1 Errors Bars-part IIIf x is the uncertainty inx, thenf, the uncertainty inf(x), is given byf=fxx-f(x).Laboratory reportData Series A - Amplitude vs. Time Steep/Shallow data t (s) A (cm) Asteep Ashallow 0.00 0.01 50 3% 51.5 48.5 1.00 0.01 45 3% 46.35 43.65 2.00 0.01 40 3% 41.2 38.8 3.00 0.01 36 3% 37.08 34.92 4.00 0.01 33 3% 33.99 32.01 5.00 0.01 30 3% 29.1 30.9 6.00 0.01 27 3% 26.19 27.81 7.00 0.01 25 3% 24.25 25.75 8.00 0.01 23 3% 22.31 23.69 9.00 0.01 21 3% 20.37 21.63 Data Series C - Force vs. Distance Steep/Shallow data r (cm) F (N) Fsteep Fshallow 2.5 0.1 4.7 0.2 4.9 4.5 3.2 0.1 3.1 0.2 3.3 2.9 3.7 0.1 2.1 0.2 2.3 1.9 5.0 0.1 1.2 0.2 1.4 1 5.2 0.1 1 .1 0.2 0.9 1.3 6.1 0.1 0.8 0.2 0.64 1.04 6.5 0.1 0.7 0.2 0.53 0.93 7.4 0.1 0.6 0.2 0.38 0.78 Data Series B - Velocity vs. Position Steep/Shallow data x (cm) v (m/s) vsteep vshallow 234 8 38 8 46 30 329 8 80 8 88 72 424 8 112 8 120 104 592 8 177 8 177 177 712 8 216 8 208 224 811 8 259 8 251 267 944 8 303 8 295 311 Data Series D - Acceleration vs. Time Steep/Shallow data t (ms) a (m/s2) asteep ashallow 12 1 15 5 20 10 21 1 22 5 27 17 29 1 30 5 35 25 43 1 49 5 49 49 56 1 86 5 81 91 69 1 141 5 136 146 87 1 269 5 264 274 Summary of results