3. Determine expressions for q(m-1,n)→(m,n), q(m+1,n)→(m,n), q(m,n+1)→(m,n) and q(m,n-1)-(m,n), forconduction associated with a control volume that spans two different materials. There is no contactresistance at the interface between the materials. The control volumes are L units long into thepage. Write the finite difference equation under steady-state conditions for node (m, n).Answer: N/AT→TAyMaterial AKA(m, n + 1) i(m1, n) (m, n)(m + 1, n)Material B(m, n1) |KB

Answered: 3. Determine expressions for…

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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Topic: Non Homogenous DE (please solve thank you!)
A higher-order differential equation given as y" + p(x)y' g (x)y = O is a homogenous equation, even if p(x) = 0. A higher-order differential equation given as y" + p(x)y' + q(x)y = 0 is also a homogenous equation, even if g(x) = 0. O Only first statement is true. O Only second statement is true. O Both first and second statements are true. O Both first and second statements are false.
Find the two-dimensional temperature distribution T(r,z) under steady state condition. Where, To=20 oC, TL=100 oC. The density, conductivity and specific heat of the material are ρ =800 kg/m3, k=200 W/m.K, and cp=2500 J/kg.K, respectively. Also, r1=10 cm and L=20 cm.
1) Obtain a state space model of the system. 2) Given m =1 kg, k = 1 N/m and b = 1 N.s/m is the system Controllable? 3) For what values of k,m,b the system is stable? Explain your answer?
Geochemical Box Models - please use same terminology found in question Consider an element X exchanging between two geochemical reservoirs A and B. Let MA and MB be the masses of X in reservoirs A and B, respectively; let tA and tB be the residence times of X in reservoirs A and B, respectively. Further let M = MA + MB be the total mass of X in the two reservoirs combined. Consider a situation where additional mass M' is injected into reservoir A at time t=0 increasing the total amount of element X in the system from M0 to M1, with no further injection at later times; further assume that tA >> tB, that the total mass in the altered system is M1 = M0 + M', and that M0 << M'. Give an expression for MB(t) as a function of M1, tA, tB, and t. What is the characteristic time for MB to approach steady state? What is the characteristic time for MA to approach steady state?
Question 4: For the system shown in Figure 1: a) Find the transfer function G(s) = X(s)/F(s). b) Find 3, wn, %OS, T,, and T,. 28 N/m x(1) 5 kg f(1) 5 N-s/m Figure 1
2. Consider a car suspension, modeled as a mass/spring/damper system (mass m, stiffness k, damping b). Suppose the height of the chassis is lo at rest, the height of the terrain below the driver varies as h(t), and the height of the chassis is denoted lo + y(t). (i.e., spring deflection away from rest is y(t) – h(t)). 2 (a) Give the transfer function G(s) = H(s) · = (b) Suppose the ground follows an oscillatory profile h(t) A cos(wx (t)) with magnitude A (in meters) and frequency w (measured in radians per meter). Suppose the car is traveling at a constant forward speed v. Using a frequency response analysis strategy, give the amplitude of oscillations experienced by the driver at steady state as a function of m, k, b, A, w, and v. Hint: You can't simply consider |G(iw)| to get the amplification in this case. (c) Suppose the ground varies by A = 5cm, w = 2 rad/m, and you are driving at v = 15 m/s. Using your answer to part (b), what amplitude of oscillation is felt by the driver when m…
The Helmholtz free energy of a liquid column that rises, due to surface tension, inside a capillary tube (Figure 1), as a function of the height, h, is given by: F(h) =(ro)gr^2h^2/2 = -2 pi sigma r h cos teta, where r is the radius of the tube, g is the local ac- celaration of gravity, is the surface tension of the liquid, and is the contact angle of the liquid in contact with the wall of the tube. (a) From this expression, obtain the value of h as a function of the other physical parameters at equilibrium.Calculate the height that water will rise in a capil-lary of diameter 0.05mm. Assume that the contactangle between the water and the tube is zero. Thesurface tension of water at experimental conditionsisσ= 7.73×10−2N/m, and the local accelarationof gravity isg= 9.7m/s2.
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1. Using Duhamel's Integral, show that the response of an undamped SDOF system subjected to step force excitation is given by the equation Po u(t) = 은 [1-cos ant] Using Duhamel's Integral, show that the response of an undamped SDOF system subjected 2. to a ramp force excitation is given by the equation sin wnt] u(t) = (Ust)o F Wntr 3. Using Duhamel's Integral, show that the response of an undamped SDOF system subjected to a step force with finite rise time excitation is given by the equation 1 u(t) = (Ust)o |1 (sin w,t – sin w, (t – t,))| Wntr Using Duhamel's Integral, show that the response of an undamped SDOF system subjected to a step force with finite rise time excitation is given by the equation 4. u(t) = (ust)o [(cos w„ (t – ta) – cos wnt)]
In a few phrases, explain any four characteristics that are particularly salient in systems of systems.

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