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PRINTER VERSION BACK End of Chapter Exercise 5.9 The following information is available for BJ Electronics Led for 2015, 2016 and 2017. 2015 2016 2017 $'000 000 $'000 000 $'000 000 Beginning Inventory 999 919 771 Ending inventory 919 771 944 Cost of sales 9,203 8,679 10,237 Sales 19,231 22,054 22,580 Required Calculate the inventory turnover ratio, days in inventory and gross profit ratio (from chapter 4) for BJ Electronics Led for 2015, 2016 and 2017. ( Round inventory turnover ratio to 2 decimal places, e.g. 9.16, days in inventory to 1 decimal place, e.g. 40.3 and gross profit ratio to 2 decimal places, (.g. 0.43.) BJ Electronics Lid 2015 2016 2017 Inventory turnover ratio Days in inventory day's days days Gross profit ratio Click if you would like to Show Work for this question: Open Show Work 10:38 PM 8/30/2020 O o searchA simply supported uniform beam under the distributed force is shown in Fig.4. The time variation of the force is a step function. Neglect damping. a) Determine the partial differential equation governing the motion u (x, /) of the this distributed mass beam. (3 points) b) We attempt a solution of the formu(x, t) =(x)q(r), substitute it into the partial differential equation and simply the equation. (4 points) c) For a uniform beam, the general solution of (x) is (x) = C, sin Bx + C, cos Bx + C; sinh Bx + C, cosh Bx. Apply the boundary conditions for this simply supported beam and determine the natural frequency @, and corresponding modes , , make the maximum value of (x) equal to 1. (10 points) d) The total displacement is given by u(x, t) = )o, (x)q, (t) . Use the orthogonality relations to derive the EOMto this form M,q, (1) +K,q, (1) = P. (t) . Determine the M,,, K, and P. (t) by substituting the natural frequency and corresponding modes. (15 points) e) Solve the modal equations M,q, (1) + K,q, (1) = P. (). (4 points) f) Determine the deflection at mid-span u( 2., ) conly cousi at (only consider first 3 modes). (5 points) [Note] -b) Let a (t) " (x) w- and B+ = - w'm q(1) mo ( x) EI -c) The bending moment can be calculated as M = EI -d) sin ax dx = - COS aX [sin ax dx = x sin 2ax a 4a -e) The solution of the SDF which with EOM mu + ku = p(f) and boundary conditions w/ (0) = 0 & (0) =0is u(t) = (1;) 1-cos(@,t)]2.4. For a beam with both ends xed as shown in Fig. P14, the equations of motion for a three-element model are obtained as follows (these will be explained in Chaplet-7): % {3 a; % 312 o 54 -13L v1 0 E! o s E 2 \"43% 0 8L" 13L ~31} 9; a 0 L \"% \"E g 0 42 54 13L 312 o v; 0 E 2 o s -13L 3L'1 0 3L2 62 0 where 131 and 122 are the deections and 31 and 62 are the slopes at points 1 and 2, respectively. Their sign conVentions are shown in Fig. P2.4. The beam is an 8123 steel I beam with the following properties: A = 6.71 in.2 I = 64.2111} L =120in. E -= 30 x 10' psi p =_D.,000733 lb-see2 in.4 " J'. I? .. (D G) I 18 x I L l I. I L I Figure P24 damped-clamped beam modeled by three beam elements. Find the four natural frequencies (ml, mg, :3, and (:34) and plot the shapes of the two modes corresponding to all and m2.'1f the subroutine 'for solving for eigenvalues and eigenvectors of a real nonsymmetiic matrix is not available in the _ system library, use NROOT and EIGEN as described in Section 2.17. Most often in Rector Physics, scattering cross-sections are expressed in terms of Legendre Polynomials. In this exercise you are expected to develop a set of cross-sections for helium, for which the atomic mass number A=4. It is also assumed that the scattering is isotropic in the center of mass (CM). However, the cross-sections employed in Reactor Physics are the cross-sections in the LAB system. In an elastic neutron scattering event, it is known that the cosine of the scattering angle ( ) in the LAB system (where the nucleus is stationary), can be expressed as the cosine of the scattering angle (uc) in (CM): 1 + A * Hc ML = - V1+ A + 2 * A *Hc Because the scattering is isotropic in the CM, the probability distribution of the cosines of the neutrons scattered from helium isotope is given by: f(He) = 1/2 for -1 S Me $ 1 a) Find the probability distribution in the LAB system f(uz). One can expand this probability distribution in terms of Legendre polynomials Pr (12 ): f( H.) =5 ) (2n+ 1)fm * Pr (12) n= Where, fo's are the expansion coefficients. b) Determine the coefficients fo, f1, f2, f3, fa, fs and fa. Instead of the infinite sum, in engineering the series expansion is often truncated at some value N. Therefore, defining: for ( ML ) = = ) ( 2n+ 1)im * Pm (12) 1=0 c) Plot f(u ) and fi(u ); plot f(u:) and f2(u); plot f(u.) and fs(); plot flu) and fa(u); plot flu.) and fs(u.); plot flu.) and fa(ML) each versus us ranging from -1 to +1. This will demonstrate that fm(ML) converges to f(ML) as N getting large. The error made in the truncation is measured by the quantity en: eN = IfN ( 12 ) - F( ML)12diz d) Evaluate eo, e1, ez, es, e4, es and es. Note: The cross sections are then expressed using the coefficients f, you have evaluated