A bar of length l (0 ≤ x ≤ ) is initially held at T = 0. After t = 0, the side at x = 0 is heldat T=0 while the other side at x = l is held at T = To. Find the time-dependent temperaturedistribution, T(x, t).

Given: length of the bar=l Temperature at x=0 is→T1=0 And temperature at x=l is→T2=To Because…

Answered: A bar of length (0 ≤ x ≤ 0) is…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

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29. The figure shows a heavy weight suspended by a cable and pulled to one side by a force F. We want to know how much force F is required to hold the weight in equilibrium at a given distance z to one side (say to place a cornerstone correctly). From elementary physics, T cos 0 W, and T sin 0 = F. (a) Find F/W as a series of powers of 0. (b) Usually in a problem like this, what we know is not 0, but a and I in the diagram. Find F/W as a series of powers of a/l.
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Suppose that the assembled stiffness matrix of question 1 (as shown below) is as follows: [K]=108×a-a0-aa+b-b0-bb where a=4.06 N/m and b=2.28 N/m. If the applied force at node 3 is P=210 KN, find the displacement of node 2 in mm?
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For this problem, take a look at Figure 2. Assume that the rod is massless, perfectly rigid, and pivoted at point P. When the rod is perfectly horizontal, the angle 0 = 0, the displacement y = 0, and the spring is in neither tension nor compression. Gravity acts on the system (e.g. on mass M). We assume that y is a small displacement. A mass M is attached at the end of the rod. k Schen a 0 a F The equation of motion for the system can be derived to be: a 4aM0+ ak0 =-F-2Mg T y M Your tasks: A. Transform the rotational equation of motion, which is in 0, given above, to another variable, y, which is zero at the static equilibrium position. B. Represent the mechanical system in state space form. Using MATLAB or a calculator (just say what you used), calculate the eigenvalues of your A matrix for the following system parameters: a = 0.25 [m], M = 1 [kg], k = 16 [N/m], and F = 0 [N]. What do the eigenvalues say about the stability of the system? C. Derive the response of the system in the…
For this problem, take a look at Figure 2. Assume that the rod is massless, perfectly rigid, and pivoted at point P. When the rod is perfectly horizontal, the angle 0 = 0, the displacement y = 0, and the spring is in neither tension nor compression. Gravity acts on the system (e.g. on mass M). We assume that y is a small displacement. A mass M is attached at the end of the rod. k Schen a 0 a F The equation of motion for the system can be derived to be: a 4aM0+ ak0 =-F-2Mg T y M Your tasks: A. Transform the rotational equation of motion, which is in 0, given above, to another variable, y, which is zero at the static equilibrium position. onical system in sta bace form. Using MATLAB or a calculator lues of INI. W 16 [N/m], and C. Derive the response of the system in the Laplace (s) domain. Use the static equilibrium value found in part A (Ost) as the initial value, (0), for the problem. Assume (0) and the force, F, are both zero. You may treat gravity as g = 10 [m/s²] for ease of…
Consider the following spring system. 直一 m, 2 with spring constants c = 5 Assume down is the positive direction. Write the elongation matrix A = Write the stiffness matrix K =

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A bar of length (0 ≤ x ≤ 0) is initially held at T = 0. After t = 0, the side at x = 0 is held at T = 0 while the other side at x = l is held at T = To. Find the time-dependent temperature distribution, T(x, t).