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 25, Problem 14P
Develop a user-friendly computer program for the classical fourth-order RK method. Test the program by duplicating Example 25.7.
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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 25 Solutions
Numerical Methods for Engineers
Ch. 25 - Solve the following initial value problem over the...Ch. 25 - Solve the following problem over the interval from...Ch. 25 - Use the (a) Euler and (b) Heun (without iteration)...Ch. 25 - Solve the following problem with the fourth-order...Ch. 25 - Solve from t=0to3withh=0.1 using (a) Heun (without...Ch. 25 - 25.6 Solve the following problem numerically from...Ch. 25 - Use (a) Eulers and (b) the fourth-order RK method...Ch. 25 - 25.8 Compute the first step of Example 25.14...Ch. 25 -
25.9 If, determine whether step size adjustment...Ch. 25 - Use the RK-Fehlberg approach to perform the same...
Ch. 25 -
25.11 Write a computer program based on Fig....Ch. 25 - Test the program you developed in Prob. 25.11 by...Ch. 25 -
25.13 Develop a user-friendly program for the...Ch. 25 - Develop a user-friendly computer program for the...Ch. 25 - Develop a user-friendly computer program for...Ch. 25 - 25.16 The motion of a damped spring-mass system...Ch. 25 - If water is drained from a vertical cylindrical...Ch. 25 - The following is an initial value, second-order...Ch. 25 - Assuming that drag is proportional to the square...Ch. 25 - A spherical tank has a circular orifice in its...Ch. 25 - The logistic model is used to simulate population...Ch. 25 - 25.22 Suppose that a projectile is launched...Ch. 25 - The following function exhibits both flat and...Ch. 25 - 25.24 Given the initial conditions,, solve the...Ch. 25 - Use the following differential equations to...Ch. 25 - 25.26 Three linked bungee jumpers are depicted in...
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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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