EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 8220100254147
Author: Chapra
Publisher: MCG
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Chapter 27, Problem 21P
The following
Transform this equation into a pair of ODEs. (a) Use MATLAB to solve these equations from t 5 0 to 0.4 for the case where
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Consider the following linear equations,
1. The general form of linear second-order differential equation can be written in the form:
و بار / كلية الهندسة
Q4)/
grap
dy
q(x)y = r(x)
d'y
+p(x)
dx
dy
b.
dx
- F(x)y = F(x)
x2 dy
dx
- xy =
C.
d. r2 d?y
dx2
-f(x)y = F(x)
2431)(5-1) 3
(3-21)2
a. (221 -91i) / 169
b. (21 + 52i)/ 13
c. (-90+220i)/169
d. (-7+17i)/ 13
2. Simplify:
الحدار المك المراغة
3. If the roots of second order differential equation is complex conjugate, then the gene
contain:
a. sinusoidal functions and exponentials
b. constant and two exponentials
c. two constants and two exponentials
d. two constants and one exponential
5
4. The order and degree of the differential: 3(3 - + 4y = sinx* are:
d²y
a. First-order, First-degree-
b. First-order, second-degree
Second -order, First -degree
d. Second -order, second-degree
dx2
lo - 2i tisi.
8- 12i
5. The particular solution of (D² + 4)y = cos 2x is equal to:
a. sin 2x
b. cos 2x
13+159
C. 4 cos 2x
d. 4 sin 2x
5-12
lo
Best wishes
الامتحانية
د. مازن ياسین عبود
رئيس القسم
بن فاضل…
please solve it in clear
note: The fifth section solved it by using MATLAB
i need all qusestion solved 1-9
For the mass spring damper system shown in the figure, assume that m = 0.25 kg, k= 2500 N/m,
and c = 10 N.s/m. The values of force measured at 0.05-second intervals in one cycle are given
below.
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
time
F(t)
time
12
14
44
19
33
34
12
22
0.60
25
0.45
0.50
0.55
0.65
0.70
0.75
0.80
0.85
Force
32
11
18
30
49
40
35
21
time
0.90
0.95
F(t)
11
m
+x
F(1)
1- Find the equation of motion.
2- Find the homogenous solution.
3- If we excite the system with initial displacement and velocity as 5 mm and 0.2 m/s
respectively, plot the response of the free vibration system.
4- Use the generated plot in part 3 to verify the value of the damping constant, c.
5- Find the steady state solution (only particular solution) for the forced vibration system.
Take number of terms in your Fourier series terms from this range [ 30 – 55).
6- Plot the force in the table, and the…
Chapter 27 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 27 - A steady-state heat balance for a rod can be...Ch. 27 - 27.2 Use the shooting method to solve Prob. 27.1....Ch. 27 - 27.3 Use the finite-difference approach with to...Ch. 27 - 27.4 Use the shooting method to solve
Ch. 27 - Solve Prob. 27.4 with the finite-difference...Ch. 27 - 27.7 Differential equations like the one solved...Ch. 27 - 27.8 Repeat Example 27.4 but for three masses....Ch. 27 - 27.9 Repeat Example 27.6, but for five interior...Ch. 27 - Use minors to expand the determinant of...Ch. 27 - 27.11 Use the power method to determine the...
Ch. 27 - 27.12 Use the power method to determine the...Ch. 27 - Develop a user-friendly computer program to...Ch. 27 - Use the program developed in Prob. 27.13 to solve...Ch. 27 - 27.15 Develop a user-friendly computer program to...Ch. 27 - Use the program developed in Prob. 27.15 to solve...Ch. 27 - 27.17 Develop a user-friendly program to solve...Ch. 27 - Develop a user-friendly program to solve for the...Ch. 27 - 27.19 Use the Excel Solver to directly solve...Ch. 27 - Use MATLAB to integrate the following pair of ODEs...Ch. 27 - The following differential equation can be used to...Ch. 27 - 27.22 Use MATLAB or Mathcad to...Ch. 27 - 27.23 Use finite differences to solve the...Ch. 27 - Solve the nondimensionalized ODE using finite...Ch. 27 - 27.25 Derive the set of differential equations for...Ch. 27 - 27.26 Consider the mass-spring system in Fig....Ch. 27 - 27.27 The following nonlinear, parasitic ODE was...Ch. 27 - A heated rod with a uniform heat source can be...Ch. 27 - 27.29 Repeat Prob. 27.28, but for the following...Ch. 27 - 27.30 Suppose that the position of a falling...Ch. 27 - Repeat Example 27.3, but insulate the left end of...
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- From the following graph identify the steady-state maximum force. 1.2 1 0.8 0.6 0.4 0.2 0 Electical Power 1 Force vs. Time 2 Time (s) m 4 5arrow_forwardConvert the following 4th order ODE into a system of four first order ODES of the form dy/dt f(t,y). Remember to account for initial conditions in the system you create. 4y"'(t) – 8y"' (t) + 2y"(t) + 16y'(t) – 4y(t) = 20e2t y(0) = 3, y'(0) = 4, y"(0) = 7 and y"'(0) = = 13 2:36 PM 73°F Mostly cloudy 3/4/2022arrow_forwardA velocity of a vehicle is required to be controlled and maintained constant even if there are disturbances because of wind, or road surface variations. The forces that are applied on the vehicle are the engine force (u), damping/resistive force (b*v) that opposing the motion, and inertial force (m*a). A simplified model is shown in the free body diagram below. From the free body diagram, the ordinary differential equation of the vehicle is: m * dv(t)/ dt + bv(t) = u (t) Where: v (m/s) is the velocity of the vehicle, b [Ns/m] is the damping coefficient, m [kg] is the vehicle mass, u [N] is the engine force. Question: Assume that the vehicle initially starts from zero velocity and zero acceleration. Then, (Note that the velocity (v) is the output and the force (w) is the input to the system): A. Use Laplace transform of the differential equation to determine the transfer function of the system.arrow_forward
- An object attached to a spring undergoes simple harmonic motion modeled by the differential equation d²x = 0 where x (t) is the displacement of the mass (relative to equilibrium) at time t, m is the mass of the object, and k is the spring constant. A mass of 3 kilograms stretches the spring 0.2 meters. dt² Use this information to find the spring constant. (Use g = 9.8 meters/second²) m k = + kx The previous mass is detached from the spring and a mass of 17 kilograms is attached. This mass is displaced 0.45 meters below equilibrium and then launched with an initial velocity of 2 meters/second. Write the equation of motion in the form x(t) = c₁ cos(wt) + c₂ sin(wt). Do not leave unknown constants in your equation. x(t) = Rewrite the equation of motion in the form ä(t) = A sin(wt + ), where 0 ≤ ¢ < 2π. Do not leave unknown constants in your equation. x(t) =arrow_forwardA velocity of a vehicle is required to be controlled and maintained constant even if there are disturbances because of wind, or road surface variations. The forces that are applied on the vehicle are the engine force (u), damping/resistive force (b*v) that opposing the motion, and inertial force (m*a). A simplified model is shown in the free body diagram below. From the free body diagram, the ordinary differential equation of the vehicle is: m * dv(t)/ dt + bv(t) = u (t) Where: v (m/s) is the velocity of the vehicle, b [Ns/m] is the damping coefficient, m [kg] is the vehicle mass, u [N] is the engine force. Question: Assume that the vehicle initially starts from zero velocity and zero acceleration. Then, (Note that the velocity (v) is the output and the force (w) is the input to the system): 1. What is the order of this system?arrow_forwardFind a vector equation and parametric equations for the line segment that joins P to Q. P(3.5, −2.4, 2.1), Q(1.8, 0.3, 2.1) vector equationr(t)= parametric equations (x(t), y(t), z(t)) =arrow_forward
- 2 0 2 5 7 11 f(x) 13 5 17 28 41 Selected values of a differentiable function f are given in the table above. What is the fewearrow_forward1. A spring mass system serving as a shock absorber under a car's suspension, supports the M=1000kgmass of the car. For this shock absorber,k=1000N/m and c=2000N s/m. The car drives over a corrugated road with force F=2000sin(wt)N. Use your notes to model the second order differential equation suited to thisapplication. Simplify the equation with the coefficient of x'' as one. Solve x (the general solution) interms of using the complimentary and particular solution method. In determining the coefficients ofyour particular solution, it will be required that you assume w2 -1=w or . Do not 1-w2=-wuse Matlab as its solution will not be identifiable in the solution entry. Do not determine the value of w.You must indicate in your solution:1. The simplified differential equation in terms of the displacement x you will be solving2. The m equation and complimentary solution3. The choice for the particular solution and the actual particular solution xp4. Express the solution x as a piecewise…arrow_forwardTwo cables AB and AC are acting on the pole with forces FAB = 540N and FAC = 560N with parameters defining the attachment points shown in the table. We want to write the vector FAB in cartesian vector form. C X Y₂ parameters value units FAB 540 FAC 560 L ZI 3 7₂ 5.5 4 3.5 4 4 Submit Question N N m m m m m FAC A Y₁ Z write the vector FAB in Cartensian Vector Notation. Round your final answers to 3 significant figures. FAB= AB B L X1 Narrow_forward
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