Numerical Methods for Engineers
7th Edition
ISBN: 9780073397924
Author: Steven C. Chapra Dr., Raymond P. Canale
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 4, Problem 23P
Repeat Example 4.8, but for the forward divided difference (Eq. 4.17).
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Assume a Space Launch System (Figure 1(a)) that is approximated as a cantilever undamped single degree of freedom (SDOF) system with a mass at its free end (Figure 1(b)). The cantilever is assumed to be massless. Assume a wind load that is approximated with a concentrated harmonic forcing function p(t) = posin(ωt) acting on the mass. The known properties of the SDOF and the applied forcing function are given below. • Mass of SDOF: m =120 kip/g • Acceleration of gravity: g = 386 in/sec2 • Bending sectional stiffness of SDOF: EI = 1015 lbf×in2 • Height of SDOF: h = 2000 inches • Amplitude of forcing function: po = 6 kip • Forcing frequency: f = 8 Hz Figure 1: Single-degree-of-freedom system in Problem 1. Please compute the following considering the steady-state response of the SDOF system. Do not consider the transient response unless it is explicitly stated in the question. (a) The natural circular frequency and the natural period of the SDOF. (10 points) (b) The maximum displacement of…
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Chapter 4 Solutions
Numerical Methods for Engineers
Ch. 4 - The following series can be used to approximate...Ch. 4 - 4.2 The Maclaurin series expansion for cos x...Ch. 4 - 4.3 Perform the same computation as in Prob. 4.2,...Ch. 4 - 4.4 The Maclaurin series expansion for the...Ch. 4 - 4.5 Use zero- through third-order Taylor series...Ch. 4 - 4.6 Use zero- through fourth-order Taylor series...Ch. 4 - Use forward and backward difference approximations...Ch. 4 - 4.8 Use a centered difference approximation of to...Ch. 4 - 4.9 The Stefan-Boltzmann law can be employed to...Ch. 4 - Repeat Prob. 4.9 but for a copper sphere with...
Ch. 4 - Recall that the velocity of the falling...Ch. 4 - 4.12 Repeat Prob. 4.11 with.
Ch. 4 - 4.13 Evaluate and interpret the condition numbers...Ch. 4 - Employing ideas from Sec. 4.2, derive the...Ch. 4 - Prove that Eq. (4.4) is exact for all values of x...Ch. 4 - Mannings formula for a rectangular channel can be...Ch. 4 - If |x|1, it is known that 11x=1+x+x2+x3+ Repeat...Ch. 4 - A missile leaves the ground with an initial...Ch. 4 - To calculate a planets space coordinates, we have...Ch. 4 - 4.20 Consider the function on the interval . Use...Ch. 4 - Derive Eq. (4.31).Ch. 4 - 4.22 Repeat Example 4.8, but for .
Ch. 4 - 4.23 Repeat Example 4.8, but for the forward...Ch. 4 - 4.24 Develop a well-structured program to compute...
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- The design of the gear-and-shaft system shown requires that steel shafts of the same diameter be used for both AB and CD. It is further required that the angle D through which end D of shaft CD rotates not exceed 1.5°. Knowing that G = 77.2 GPa, determine the required diameter of the shafts. 40 mm 400 mm 100 mm 600 mm T-1000 N-m Darrow_forwardAssume a Space Launch System (Figure 1(a)) that is approximated as a cantilever undamped single degree of freedom (SDOF) system with a mass at its free end (Figure 1(b)). The cantilever is assumed to be massless. Assume a wind load that is approximated with a concentrated harmonic forcing function p(t) = posin(ωt) acting on the mass. The known properties of the SDOF and the applied forcing function are given below. • Mass of SDOF: m =120 kip/g • Acceleration of gravity: g = 386 in/sec2 • Bending sectional stiffness of SDOF: EI = 1015 lbf×in2 • Height of SDOF: h = 2000 inches • Amplitude of forcing function: po = 6 kip • Forcing frequency: f = 8 Hzarrow_forward13.44 The end of a cylindrical liquid cryogenic propellant tank in free space is to be protected from external (solar) radiation by placing a thin metallic shield in front of the tank. Assume the view factor Fts between the tank and the shield is unity; all surfaces are diffuse and gray, and the surroundings are at 0 K. Tank T₁ Shield, T T₁ = 100 K E1 Solar irradiation Gs ε₁ = ε₂ = 0.05 ε₁ = 0.10 Gs = 1250 W/m² E2 Find the temperature of the shield T, and the heat flux (W/m²) to the end of the tank.arrow_forward
- question 664 thank youarrow_forward13.38 Consider the attic of a home located in a hot climate. The floor of the attic is characterized by a width of L₁ = 8 m while the roof makes an angle of 0 = 30° from the horizontal direction, as shown in the schematic. The homeowner wishes to reduce the heat load to the home by adhering bright aluminum foil (ε = 0.07) onto the surfaces of the attic space. Prior to installation of the foil, the surfaces are of emissivity & = 0.90. Attic A2, 82, T2 0 = 30° A1, E1, T₁ 土 L₁ = 8 m (a) Consider installation on the bottom of the attic roof only. Determine the ratio of the radiation heat transfer after to before the installation of the foil. (b) Determine the ratio of the radiation heat transfer after to before installation if the foil is installed only on the top of the attic floor. (c) Determine the ratio of the radiation heat transfer if the foil is installed on both the roof bottom and the floor top.arrow_forward13.1 Determine F2 and F2 for the following configura- tions using the reciprocity theorem and other basic shape factor relations. Do not use tables or charts. (a) Small sphere of area A, under a concentric hemi- sphere of area A₂ = 3A₁ A₂ A1 (a) (b) Long duct. Also, what is F₁₂? A₂ Αν (b) (c) Long inclined plates (point B is directly above the center of A₁) B 100 mm A₂ - 220 mm (c) (d) Long cylinder lying on infinite plane + A₁ Az (d) (e) Hemisphere-disk arrangement -A₂, hemisphere, diameter D A₂ A₁, disk, diameter D/2 (e) (f) Long, open channel 1 m AA₂ 2 m (f) (g) Long cylinders with A₁ = 4A₁. Also, what is F₁₂? -D₁ A1 -A₂ -D2 (e) (h) Long, square rod in a long cylinder. Also, what is F22? w=D/5 18 A₁ -A2 (h) -Darrow_forward
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