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A pentadiagonal system with a bandwidth of five can be expressed generally as
Develop a program to efficiently solve such systems without pivoting in a similar fashion to the algorithm used for tridiagonal matrices in Sec. 11.1.1. Test it for the following case:
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Chapter 11 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
- The wavefunction for the ground state of a hydrogen atom is Ne-r/a0. Evaluate the normalization constant N.arrow_forwardLight from a source A at (−1, 1) is reflected by a plane mirror placed along the x-axisto a receiver B at (2, 2).(a) For a given point (x, 0) between A and B on the x-axis, find the distance betweenA and (x, 0) and the distance between B and (x, 0). Your answers should dependon x.(b) Denote by D(x) the sum of the two distances you found in the part (a), thoughtof as a function of x. Find D0(x).(c) Find the absolute minimum of D(x) on the x-interval [−1, 2].(d) The light from source A reflected by the mirror to receiver B will travel theshortest distance possible (more precisely, light will obey Fermat’s principle). Atwhat point P on the x-axis between A and B does the light hit the mirror?arrow_forwardWhat is an S-N Wöhler diagram? how to draw what does it do?arrow_forward
- FIND moments around O, A and B SOON 90ON 60 В 4m A 5marrow_forwardIn the far-infrared spectrum of 39K³5Cl(g), there is an intense line at 278.0 cm²¹. Calculate the force constant (in) and the period (in sec) of vibration of 39K³5Cl(g).arrow_forward1. What is the total flux passing through a 10 cm x 6 cm surface in a region where the electric flux density is 2700 µC/m? ? [1.62 x 105 C]arrow_forward
- RC-2 A half ring of charge lies in the x-z plane with its center at the origin as shown to the right. There are λ coulombs per meter of charge evenly distributed along the ring, which has radius 'a'. a) Sketch on your paper figures like the figures shown to the right. On your figures show an arrow representing the electric field at the point P that is produced by source charge element dq. I TI Cul 3D view: zl (C/m) X a b View looking from point P toward the origin: yarrow_forwardFor an Einstein solid with four oscillators and two units of energy, represent each possible microstate as a series of dots and vertical lines, as used in the text to prove equation 2.9.arrow_forwarddetermine the x and y components of 4 n as shown in figure belowarrow_forward
- A 4.0-nm-diameter protein is in a 0.050 M KCl solution at 25° C. The protein has 9 positive and 20 negative charges. Model the protein as a sphere with a uniform surface charge density. Part A What is the electric potential of the protein at the surface? Express your answer with the appropriate units. μA ? Vsurface = Value Units Submit Request Answer Part B What is the electric potential of the protein 2.0 nm from the surface? Express your answer with the appropriate units. με V2 nm = Value Units Submit Request Answerarrow_forwardDetermine the electric potential at a position z along the axis of a cone. The cone has uniform surface charge density σ, total height h and radius R at its top as shown. The relative proportions of the height and radius of the opening are such that the angle of the cone is 45°. You will not be able to evaluate the resulting integral analytically, so your final answer is the integral expression. (Please type answer no write hy hend)arrow_forwardA musical note on a piano has a frequency of 40 Hz. If the tension in the 2-m string is 308 N, and one-half wavelength occupies the string, what is the mass of the wire? O 0.040 kg 0.047 kg 0.031 kg 0.019 kg 0.024 kgarrow_forward
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