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mws_mec_nle_txt_bisection_examples

mws_mec_nle_txt_bisection_examples - Chapter 03.03...

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Chapter 03.03 Bisection Method of Solving a Nonlinear Equation- More Examples Mechanical Engineering Example 1 A trunnion has to be cooled before it is shrink fitted into a steel hub. Figure 1 Trunnion to be slid through the hub after contracting. The equation that gives the temperature to which the trunnion has to be cooled to obtain the desired contraction is given by f T 0 10 88318 . 0 10 74363 . 0 10 38292 . 0 10 50598 . 0 ) ( 2 4 2 7 3 10 T T T T f f f f f f T Use the bisection method of finding roots of equations to find the temperature to which the trunnion has to be cooled. Conduct three iterations to estimate the root of the above equation. Find the absolute relative approximate error at the end of each iteration and the number of significant digits at least correct at the end of each iteration. Solution From the designer’s records for the previous bridge, the temperature to which the trunnion was cooled was . Hence assuming the temperature to be between and F 108 F 100 F 150 , we have F 150 , f T , F 100 , u f T Check if the function changes sign between and . , f T u f T , 03.03.1
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