Q1:- Determine the steady state temperature at six nodes for steady-state heatconduction in a rectangular section 0

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Answered: Q1:- Determine the steady state…

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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4. A cup of coffee has a temperature of 80°C when it is placed outside where the temperature is 20˚C. Suppose the temperature of the coffee, T(t), changes according to Newton's Law of Cooling with proportionality constant k = 0.09. (a) Find and classify the equilibrium solution(s) using a phase line. (b) Find T(t). (c) Evaluate and interpret lim T(t). t→∞
1. Let {yt} be SARIMA(0, 0, 2) × (0, 0, 1)12 with MA coefficients 0.2, 0.3, seasonal MA coefficient 0.5 and Et~ WN(0, ²) with o² = 1. Which of the following equation(s) governs {yt}? yt = (1+0.2L + 0.3L²)(1+0.5L¹2) et Yt et +0.2et-1 +0.3€t-2 +0.5et-12 +0.1et-13 +0.15€t-14 Yt +0.2yt-1+0.3yt-2 +0.5yt-12 +0.1yt-13 +0.15yt-14 = €t Yt = (1+0.2L + 0.3L² +0.5L¹2 +0.1L¹³ +0.15L¹4) et
Figure 1.5.7 shows a slope field and typical solution curves for the equation y' = x – y. (a) Show that ev- ery solution curve approaches the straight line y = x – 1 as x → +oo. 10 -6- -10 H FIGURE 1.5.7. Slope field and solution curves for y' = x – y.
1. a) Using undetermined coefficients, give the general solution to y" + 4y = 9 cos t. b) Use your solution from Part la to find the exact solution to the IVP: y" + 4y = 9 cos t, y(0) = 3, y'(0) = 4 and find y(10) correct to six decimal places. c) Make a plot of your solution in part b for 0
4.4
As a spring is heated, its spring "constant" decreases. Suppose the spring is heated so that the spring "constant" at time t is k(t) = 9-t N/m. If the unforced mass-spring system has mass m = 2 kg and a damping constant b = 1 N-sec/m with initial conditions x(0) = 2 m and x'(0) = 0 m/sec, then the displacement x(t) is governed by the initial value problem 2x" (t) +x' (t) + (9 − t)x(t) = 0; x(0) = 2, x'(0) = 0. Find the first four nonzero terms in a power series expansion about t = 0 for the displacement. x(t) = ☐ +... (Type an expression that includes all terms up to order 4.) k(t)=9-t mrr 1 N-sec/m 2 kg heat x(t) x(0)=2 x'(0)=0

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Q1:- Determine the steady state temperature at six nodes for steady-state heat conduction in a rectangular section 0