a² ua² u+ = 0 and find U₁, U2, U3, U4 bydy²əx²Gauss-Seidal method? Use x=0=y, x=3=yProblem 3.1: Solve the Laplace equation1000200020001000MAS1000U₂5001000S10005000O

As per the question, we are given the nodal values of a function U(x,y) at 16 points. We are…

Answered: a² u a² u 3.1: Solve the Laplace…

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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Fnd the position vector for a particle with accelerationy inttal velocity, and initial position given below (, 2 sin(t), cos(6t)) 7(0) = (5, 5,- 2 车 5t 2 sinit) cosi it 36 Question Heip: Video
H1. Consider a point particle with position vector r= (x, y, z) in Cartesian coordinates, moving with a velocity v = (B, az, -ay), where a and ẞ are positive constants. (a) What are the physical dimensions of a and B? (b) Find the general form of r(t), the position of the particle, as a function of time t, assuming the initial position of the particle is ro = (0,2,0). (hint: write v = (B, az, -ay) as a system of first order ODEs and note that the equation for x is decoupled from the others). Describe in words the motion of the particle and sketch its trajectory in R³ (you can use software packages for the plot). (c) Show that the speed of the particle is constant, but the acceleration vector a(t) is nonzero. Justify. (d) Assuming the particle has a constant mass m, use Newton's second law to show that force acting on the particle is (as a function of the position r = (x, y, z)) F(x, y, z) = ma² (0, -y, -z).
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a² u a² u 3.1: Solve the Laplace equation + = 0 and find U₁1, U2, U3, U4 by əx² dy² Gauss-Seidal method? Use x=0=y, x=3=y 1000 2000 2000 1000 1000 U₂ 5 U₂ 500 1000 S 1000 500 0 O