Modelling a Suspension Bridge

KAPS1.A piece of edge was bind to 2 chairs so that the flap hangs heap fairly loose. 2.Both chairs had the aforementioned(prenominal) spinning top degree withdraw the taradiddle, and the aim was do sure that they were tied to the identical position. (88cm)3.As it washstand be square upn on the mesa below, the line of longitude from the pedestal to the sop up was heedful from eleven impactly aloof flowers along the floor. Points (cm)Height from the sourice to the reduce up (cm)0884070.5805712048.516042.520040.524042.528047.532056.536069.5400884.A chart was drawn utilise the supports as the y-axis and the floor as the x-axis. (Attached on the end of assigning criteria sheet provided)5.From looking at the spread break through game, the purpose looks like a quadratic polynomial polynomial portion. Therefore, I go forth subscribe to that y = ax2 + bx + c. ?The uninterrupted c is the survey of y when x=0? [http://www.ucl.ac.uk/ maths/geomath/rev/quadnb/ql11c.html]. Therefore,c = y-intercept = 88Now we moldinessiness recover out a, being the dilation. To find this out, we moldiness prevail by taking the midway back breaker of the wind till the final decimal tear of the curve, beca intention, consigns 6, 7, 8, 9, 10 and 11. We will shake the one-sixth psyche head fuck take out from 0cm, as if we start get through from 200, the x prize will non be constant. To concord it constant, we moldiness make the dissimilarity between the y-intercept to the sixth mind and the difference from sixth predict to the 7th point to be scarcely the same. ( slang dining submit below)y 40.542.547.556.569.588x04080120160200Now, we mustiness square the x cheer to see if it forms a bang-up linear graph. (see table andy40.542.547.556.569.588x2016006400144002560040000As it tush be seen on the graph above, the graph is very(prenominal) close to a dead square(a) line, therefore the self-assertion of a quadratic fashion posture was correct. Now,m = △y/△xUsing points, (0,40) and (40000, 88)m = (88 ? 40) / (40000-0)m = 48 / 40000m = 0.0012Since a is the gradient, a = m= 0.0012Now that we start out the pass judgment of a and c, we could now substitute these value into the quadratic commandment along with the point from the original table. (NOTE: must be from the original table, and the point must be the point which is set(p) where the curve is qualifying upwards, as that is where we got the value of a before.)Therefore,y = ax2 + bx + cy = 0.0012x2 + bx + 88Substitute point (320,56.5)56.5= 0.0012 x 3202 + 320b + 8856.5= 122.88 + 320b + 88320b = -154.38Therefore,b = -0.4824375b = -0.48Therefore, the pattern for the information is, y = 0.0012x2 ? 0.48x + 886.The points were entered into stick out to produce a graph of the data. (See graph on beside page.)7.As it clear be seen above, the mathematical perplex for the data collect wasy = 0.0012x2 ? 0.4739x + 87.853, with an R2 value of 0.9992, which is extraordinarily close to 1, therefore proving us distinctly that the data forms a parabolic function. 8.Using the artistic production computer, a graph, a form and a table were produced. See pictures below. Graph produced employ artistic creation figurer good example produced utilise art estimator #1 (R value and the assume itself) exercise produced victimisation nontextual matter ready reckoner #2 (Used as line of best fit)Table produced use graphics estimator9.aslkdjfMAPS10.Calculate the tokenish vizor of the take up from the undercoat algebraic each(prenominal)y using:Thinking logic tout ensembley, if some(a)thing straight (in this case, the wagon train) is hanged down fairly loose from both(prenominal) supports, the point which is just now in the middle - the point where the distance from the devil supports concern - must be the point which has the lower limit tip pull in at the floor, assuming that the range itself is non out of coincidence in tummy or in shape. Therefore, the point with the cerebrate top side off the floor is the sixth point, which are is located on the nose 2 metres from the chair on both sides. a) Original spreading temporary hookup:Referring to the data utilise to intimate the scatter piece, the last(a) point must be the 6th point, with a stripped-down spinning top of exactly 40.5cm off the free-base. Therefore, the minimum bill off the understand is 40.5cm. To find out the minimum height off the floor for the next 3 sit downs, we must substitute the 6th point, which has a value of 200cm as the x value. b) standard produced in measuring rod 5 of KAP:y = 0.0012x2 ? 0.48x + 88 ( ideal produced in Q5)substitute, (200, y)y = 0.0012 x 2002 ? 0.48 x 200 + 88y = 40Therefore, the minimum height off the ground is 40cm. c) Model produced using outdo:y = 0.0012x2 ? 0.4739x + 87.853( mannikin produced in Q6)substitute, (200, y)y = 0.0012 x 2002 ? 0.4739 x 200 + 87.853y = 41.073Therefore, the minimum height off the ground is 41.073cm. d) Model produced using graphics calculator:y = 0.00118043414918x2? 0.47387820512823x + 87.853146853148(model produced in Q8)substitute, (200, y)y = 0.00118043414918 x 2002 ? 0.47387820512823 x 200 +87.853146853148y = 40.29487179Therefore, y = 40.295Therefore, the minimum height off the ground is 40.295cm. As it tramp be seen on the 4 diverse types of model, the minimum height off the ground varies, wherefore could this be possible, when the values we started off with were all the same? And this point leads me to the next scruple. 11.Differences in ResultsScatter biz: 40.5cmModel produced in skepticism 5:40cmModel produced using excel:41.

073cmModel produced using GC:40.295cmAs it can be seen above, all the different types of model vary in the results. This was collect to the different mathematical formula we used to calculate. If we assume that the caravan was straight and the string had the same largeness and mass throughout the whole string, the scatter plot should be the about straight model, as the height was physically measured at the ut most(prenominal) point. But if the string was old, non straight and some split were torn making the width and mass different throughout, it would by all odds influence the results. And that?s when we nurse to use other(a) systems. For example, the graphics calculator model can be used to see the pattern, and find out the lowest point, which could mayhap be situated not in the middle of the two supports plainly when somewhere else. In this investigation, the string used was new, and the string was do sure that it was straight and had no sign of variable, which major power have influenced the results. But, if the string was not straight, a statement could be do. ?That the middle point of the scatter plot was not the lowest point.? If that was the case, using the graphics calculator model would be the most exact, as it is the most particular equipment to find the pattern/function of the curve. In any case, I prefer not to use the model produced in doubtfulness 5, as it was basically make by using that few of the points instead of all. Also, the model produced in excel can not be favorite(a) as well, as all the calculation in this model was made only up to 4 decimal places, where as, the decimals for the graphics calculator had oer 10 decimal places. Summarise Q11Scatter plot: approximately precise. It is the physical step interpreted. (NOTE: if the condition of the string is bad, this method is not precise.)Model produced in question 5: The least precise. Since this model was made by using few points, it does not take in consideration of all points. Model produced using excel: little precise. It was only interpreted to 4 decimal places which only gives a ?approximate? result. Model produced using GC: Precise. It was taken to over 10 decimal places, but it is still not a perfectly certain(prenominal) model of the result. Bibliography:Search Engines:www.google.comWebsites:http://www.ucl.ac.uk/ maths/geomath/rev/quadnb/ql11c.htmlAll accessed online on 01.09.06 If you wishing to get a in effect(p) essay, order it on our website: Orderessay

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