EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 9780100254145
Author: Chapra
Publisher: YUZU
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Textbook Question
Chapter 11, Problem 2P
Determine the matrix inverse for Example 11.1 based on the LU decomposition and unit
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Please show all steps and write out the answer instead of typing it out, thanks
PROBLEM 1: A 12-lb rod ABC is impacted by a 2-lb object DE as shown. The
object embeds into the end of the rod at point C, determine immediately after the
impact
(a) the angular velocity of the rod ABC,
(b) the angular acceleration of the rod ABC,
A
2
B
Unit: ft
(c) the components of the reaction at B.
12
Assume that the object and the rod move as a single body after the impact.
Vo
= 35 ft/s
C
E
D
6
Please answer both questions clearly thanks
Chapter 11 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 11 - 11.1 Perform the same calculations as in (a)...Ch. 11 - Determine the matrix inverse for Example 11.1...Ch. 11 - 11.3 The following tridiagonal system must be...Ch. 11 - 11.4 Confirm the validity of the Cholesky...Ch. 11 - Perform the same calculations as in Example 11.2,...Ch. 11 - Perform a Cholesky decomposition of the following...Ch. 11 - Compute the Cholesky decomposition of...Ch. 11 - Use the Gauss-Seidel method to solve the...Ch. 11 - Recall from Prob. 10.8, that the following system...Ch. 11 - 11.10 Repeat Prob. 11.9, but use Jacobi...
Ch. 11 - 11.11 Use the Gauss-Seidel method to solve the...Ch. 11 - Use the Gauss-Seidel method (a) without relaxation...Ch. 11 - 11.13 Use the Gauss-Seidel method (a) without...Ch. 11 - Redraw Fig. 11.5 for the case where the slopes of...Ch. 11 - 11.15 Of the following three sets of linear...Ch. 11 - Use the software package of your choice to obtain...Ch. 11 - Given the pair of nonlinear simultaneous...Ch. 11 - An electronics company produces transistors,...Ch. 11 - Use MATLAB or Mathcad software to determine the...Ch. 11 - Repeat Prob. 11.19. but for the case of a...Ch. 11 - 11.21 Given a square matrix , write a single line...Ch. 11 - Write the following set of equations in matrix...Ch. 11 - In Sec. 9.2.1, we determined the number of...Ch. 11 - 11.24 Develop a user-friendly program in either a...Ch. 11 - 11.25 Develop a user-friendly program in either a...Ch. 11 - Develop a user-friendly program in either a...Ch. 11 - As described in Sec. PT3.1.2, linear algebraic...Ch. 11 - A pentadiagonal system with a bandwidth of five...
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- PROBLEM 2: A baseball catcher includes a 6-kg rod with a small net of negligible mass at point B. A spring of unstretched length 0.3 m is attached to the midpoint of bar AB at one end and to stationary point D at the other. A stopper at point E keeps the catcher in the vertical position before the pitch. Knowing the catcher just barely rotates when it catches a fastball of mass 0.18 kg, determine the required spring constant of the spring. Given = 1.5 m. Bonus: Develop a MATLAB program to solve for this problem. v₁ = 40 m/s Unit: m 1 B L E A D www wwwwwww -L-arrow_forwardQ5: Discuss the stability critical point of the ODEs x + (*)² + 2x² = 2 and draw the phase portrait. (10M)arrow_forwardNo chatgpt pls will upvotearrow_forward
- Q/By using Hart man theorem study the Stability of the critical points and draw the phase portrait of the system:- X = -4x+2xy - 8 y° = 4y² X2arrow_forwardФ sketch stability x= -4x + 2xy - 8 y° = 4 y 2 - x² чуг.arrow_forward2 Q/Given H (x,y) = x² + y² - y² Find the Hamiltonian System and prove it is first integral-arrow_forward
- Q2) A: Find the region where ODEs has no limit cycle: x = y + x³ y=x+y+y³ 6arrow_forwardQ3)A: Given H(x,y)=x2-x+ y²as a first integral of an ODEs, find this ODES corresponding to H(x,y) and show the phase portrait by using Hartman theorem and by drawing graph of H(x,y)-e. Discuss the stability of critical points of the corresponding ODEs.arrow_forwardQ/ Write Example is First integral but not Conservation system.arrow_forward
- Q/ solve the system X° = -4X +2XY-8 y°= 2 4y² - x2arrow_forwardQ4: Discuss the stability critical point of the ODES x + sin(x) = 0 and draw phase portrait.arrow_forwardUsing Karnaugh maps and Gray coding, reduce the following circuit represented as a table and write the final circuit in simplest form (first in terms of number of gates then in terms of fan-in of those gates). HINT: Pay closeattention to both the 1’s and the 0’s of the function.arrow_forward
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