Problem Set for Group 5 : Lagrange's Interpolation Question 1 Miss Mimi is an engineer who designs cryogenic chambers for extreme cooling purposes. In an experiment, she measured the average hourly temperature inside a chamber and found that maximum average temperature inside the chamber occurred about 3 hours after the chamber was switched on. The following are data measured by Miss Mimi: Time, / (Hour) 2 Temperature, T (°C) -33.696 -3.596 7.904 6.804 (a) Generate a third-order polynomial using the Lagrange's Interpolating Polynomial method to find an expression for the variation of the temperature against time, in the form of T(t) = At³+ Bt² + Ct + D, where A, B, C, and D are constants. (b) Based on the third-order polynomial generated in part (a), calculate the maximum temperature inside the chamber.
Problem Set for Group 5 : Lagrange's Interpolation Question 1 Miss Mimi is an engineer who designs cryogenic chambers for extreme cooling purposes. In an experiment, she measured the average hourly temperature inside a chamber and found that maximum average temperature inside the chamber occurred about 3 hours after the chamber was switched on. The following are data measured by Miss Mimi: Time, / (Hour) 2 Temperature, T (°C) -33.696 -3.596 7.904 6.804 (a) Generate a third-order polynomial using the Lagrange's Interpolating Polynomial method to find an expression for the variation of the temperature against time, in the form of T(t) = At³+ Bt² + Ct + D, where A, B, C, and D are constants. (b) Based on the third-order polynomial generated in part (a), calculate the maximum temperature inside the chamber.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Problem Set for Group 5: Lagrange's Interpolation
Question 1
Miss Mimi is an engineer who designs cryogenic chambers for extreme cooling purposes. In an
experiment, she measured the average hourly temperature inside a chamber and found that maximum
average temperature inside the chamber occurred about 3 hours after the chamber was switched on. The
following are data measured by Miss Mimi:
Time, / (Hour)
2
Temperature, T (°C) -33.696 -3.596
3
7.904 6.804
(a) Generate a third-order polynomial using the Lagrange's Interpolating Polynomial method to find
an expression for the variation of the temperature against time, in the form of T(t) = At³ +
Bt² + Ct + D, where A, B, C, and D are constants.
(b) Based on the third-order polynomial generated in part (a), calculate the maximum temperature
inside the chamber.
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