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Consider an insulated uniform metal rod of length T with exposed ends and with thermal diffusivity 1. Suppose that at t = 0, the temperature profile is e (x, 0) = 10 + sin 3x + 20 sin 5x + 2 sin 7x, but then the ends are held in ice at 0° C. When t is large, the temperature profile is closely approximated by a sinusoidal function of x whose amplitude is decaying to 0. What is the angular frequency of that sinusoidal function? (Hint: Start with the general solution to the heat equation with boundary conditions, and then match it to the given initial condition.)

Consider an insulated uniform metal rod of length T with exposed ends and with thermal diffusivity 1. Suppose that at t = 0, the temperature profile is e (x, 0) = 10 + sin 3x + 20 sin 5x + 2 sin 7x, but then the ends are held in ice at 0° C. When t is large, the temperature profile is closely approximated by a sinusoidal function of x whose amplitude is decaying to 0. What is the angular frequency of that sinusoidal function? (Hint: Start with the general solution to the heat equation with boundary conditions, and then match it to the given initial condition.)

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Consider an insulated uniform metal rod of length T with exposed ends and with thermal diffusivity 1. Suppose that at t = 0, the temperature profile is 0 (x,0) = 10 + sin 3x + 20 sin 5x + 2 sin 7x, but then the ends are held in ice at 0° C. When t is large, the temperature profile is closely approximated by a sinusoidal function of x whose amplitude is decaying to 0. What is the angular frequency of that sinusoidal function? (Hint: Start with the general solution to the heat equation with boundary conditions, and then match it to the given initial condition.)
Transcribed Image Text:Consider an insulated uniform metal rod of length T with exposed ends and with thermal diffusivity 1. Suppose that at t = 0, the temperature profile is 0 (x,0) = 10 + sin 3x + 20 sin 5x + 2 sin 7x, but then the ends are held in ice at 0° C. When t is large, the temperature profile is closely approximated by a sinusoidal function of x whose amplitude is decaying to 0. What is the angular frequency of that sinusoidal function? (Hint: Start with the general solution to the heat equation with boundary conditions, and then match it to the given initial condition.)
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