3. McIntyre Problem 6.22: A beam of particles is described by the wavefunction SA eipoz/(6 –...
Problem 3 (10 pts) The wavefunction of a particle in an infinite potential well, of width a, is initially given by 16 ?(x, t-0) sin"(? x/a) cos(nx/a) Find the expression for ?(x, t) for all t > 0
Problem 1. Wave function An electron is described by a wave function: for x < 0 *(z) = { ce Ce-s/1(1 – e-3/4) for x > 0 : where I is a constant length, and C is the normalization constant. 1. Find C. 2. Where an electron is most likely to be found; that is, for what value of x is the prob: bility for finding electron largest? 3. What is the average coordinate 7 of the electron? 4. What...
differential equations
Problem 2 Solve y"+y= ſt/2, if 0 <t<6, if t > 6 y(0) = 6, 7(0) = 8
< HW #1 Section 1.2 Problem 1.15 〈: 4015 〉 The beam supports the triangular distributed load shown below with wax605 lb/ft. The reactions at A and B are vertical. 6 ft 6 ft 6 ft 4.5 ft 4.5 ft Part A Determine the resultant internal loadings on the cross section at point C. Express your answers, separated by commas, to three significant figures kip, kip, kip ft Submit Provide Feedback Next >
8. Consider ar? +5 I <3 f(0) = 12.c +b > 3 Determine a and b such that f is continuous and differentiable at x = 3. )={
Problem 6 A bilinear pairing on R2 is given on basis vectors by <ei, ei >= 13; <ei, e2 >=< e2, ej >= 7; <e2,e2 >= 26 a) [3 pts) Find the matrix representation of the pairing. b) (4 pts) Explain why the bilinear pairing defines an inner product. c) [3 pts) If v = [5 – 3]T, find a non-zero vector w with < v, w >= 0
Section 5.5 Orthonormal Sets: Problem 6 Previous Problem Problem List Next Problem 1 (1 point) Use the inner product < f, g >= . f(x)g(x)dx in the vector space C°[0, 1] to find the orthogonal projection of f(x) = 6x2 + 1 onto the subspace V spanned by g(x) = x - and h(x) = 1. projy(f) =
2. Draw a possible graph of the function described: (6 pts.) 10 O 00 07 f(-3)=4, f (2)=0 f'(-4)= f'(2) = f'(9)=0) f'>0 when x < -4 and x > 2 f' <0 when - 4<x<2 f">0 when -1<x< 5 or 9<x<10 f" <0 when x < -1 or 5<x< 9 or x >10 4 N NH -10 -8 -6 -4 -2 -2 4 07 8 10 -4 -6 -8 -10
Problem 3 (20 pts) Draw the shear and moment diagrams for the beam, and determine the shear and moment in the beam as functions of x for 0cxe4 ft, 4 ftcx<10 ft and 10 ft <x< 14 ft 250 lb 250 lb 150 lb/ft -4ft
Problem 9.67 < 3 of 3 > Review Part A Locate the centroid y of the cross-sectional area of the beam constructed from a channel and a plate. Assume all comers are square and neglect the size of the weld at A. Take a = 345 mm, b = 365 mm (Figure 1) Express your answer to three significant figures and include the appropriate units. Figure < 1 of 1 > CH HÅR 7 - Value O 2 ? Units...