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 26, Problem 14P
Given the first-order ODE
Solve this stiff differential equation using a numerical method over the time period
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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
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
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wwwwwww
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Chapter 26 Solutions
Numerical Methods for Engineers
Ch. 26 - Given dydx=200,000y+200,000exex (a) Estimate the...Ch. 26 - Given dydx=30(costy)+3sint If y(0)=1, use the...Ch. 26 - 26.3 Given
If, obtain a solution from using a...Ch. 26 - Solve the following initial-value problem over the...Ch. 26 - Repeat Prob. 26.4, but use the fourth-order Adams...Ch. 26 - Solve the following initial-value problem from...Ch. 26 - Solve the following initial-value problem from...Ch. 26 - Solve the following initial-value problem from...Ch. 26 - Develop a program for the implicit Euler method...Ch. 26 - 26.10 Develop a program for the implicit Euler...
Ch. 26 - Develop a user-friendly program for the...Ch. 26 - 26.12 Use the program developed in Prob. 26.11 to...Ch. 26 - 26.13 Consider the thin rod of length l moving in...Ch. 26 - Given the first-order ODE dxdt=700x1000etx(t=0)=4...Ch. 26 - 26.15 The following second-order ODE is...Ch. 26 - 26.16 Solve the following differential equation...
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Similar questions
- Q5: Discuss the stability critical point of the ODEs x + (*)² + 2x² = 2 and draw the phase portrait. (10M)arrow_forwardNo chatgpt pls will upvotearrow_forwardQ/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_forward
- Q3)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_forwardQ/ solve the system X° = -4X +2XY-8 y°= 2 4y² - x2arrow_forward
- Q4: 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_forwardRecall the RSA encryption/decryption system. The following questions are based on RSA. Suppose n (=15) is the product of the two prime numbers 3 and 5.1. Find an encryption key e for for the pair (e, n)2. Find a decryption key d for for the pair (d, n)3. Given the plaintext message x = 3, find the ciphertext y = x^(e) (where x^e is the message x encoded with encryption key e)4. Given the ciphertext message y (which you found in previous part), Show that the original message x = 3 can be recovered using (d, n)arrow_forward
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