Control Systems Engineering
7th Edition
ISBN: 9781118170519
Author: Norman S. Nise
Publisher: WILEY
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Textbook Question
Chapter 2, Problem 32P
For each of the rotational
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29. Write, but do not solve, the equations of motion for
the translational mechanical system shown in Figure
P2.15. [Section: 2.5]
K = 5 N/m
M3 = 3 kg
fy =2 N-s/m-
fvz = 3 N-s/m
K2 = 4 N/m
o R)
K3 = 4 N/m
M, =4 kg-
M2 = 5 kg
fv, = 2 N-s/m
Frictionless
x1(1)
FIGURE P2.15
32. For the rotational mechanical system with gears
shown in Figure P2.18, find the transfer function,
G(s) = 03(s)/T(s). The gears have inertia and bear-
ing friction as shown. [Section: 2.7]
T(t)
to
|N1
小D
N2
N3
2, D2
Jz, D3 03(1)
N4
J4. D4
J5. D5
FIGURE P2.18
sair
For the mechanism shown in Figure P3.13
(a) Draw the velocity polygon (1 in = 10 in/sec)
(b) Specify velocity of points: B, C, D Specify angular velocity of links: 3, 4
Chapter 2 Solutions
Control Systems Engineering
Ch. 2 - Prob. 1RQCh. 2 - Prob. 2RQCh. 2 - Prob. 3RQCh. 2 - Define the transfer function.Ch. 2 - Prob. 5RQCh. 2 - What do we call the mechanical equations written...Ch. 2 - If we understand the form the mechanical equations...Ch. 2 - Why do transfer functions for mechanical networks...Ch. 2 - What function do gears perform?Ch. 2 - What are the component parts of the mechanical...
Ch. 2 - The motor’s transfer function relates armature...Ch. 2 - Summarize the steps taken to linearize a nonlinear...Ch. 2 - Prob. 1PCh. 2 - Prob. 2PCh. 2 - Prob. 3PCh. 2 - Prob. 4PCh. 2 - Prob. 5PCh. 2 - Prob. 6PCh. 2 - Prob. 7PCh. 2 - A system is described by the following...Ch. 2 - For each of the following transfer functions,...Ch. 2 - Write the differential equation for the system...Ch. 2 - Write the differential equation that is...Ch. 2 - Prob. 12PCh. 2 - Use MATLAB to generate the MATLAB ML transfer...Ch. 2 - Repeat Problem 13 for the MATLAB following...Ch. 2 - Use MATLAB to generate the partial fraction...Ch. 2 - Use MATLAB and the Symbolic Math Symbolic Math...Ch. 2 - Prob. 17PCh. 2 - Prob. 18PCh. 2 - Prob. 19PCh. 2 - Repeat Problem 19 using nodal equations. [Section:...Ch. 2 - Prob. 22PCh. 2 - Prob. 23PCh. 2 - Prob. 24PCh. 2 - Prob. 25PCh. 2 - Prob. 26PCh. 2 - Prob. 27PCh. 2 - Prob. 28PCh. 2 - Prob. 29PCh. 2 - Write, but do not solve, the equations of motion...Ch. 2 - For the unexcited (no external force applied)...Ch. 2 - For each of the rotational mechanical systems...Ch. 2 - For the rotational mechanical system shown in...Ch. 2 - Find the transfer function, 1sTs , for the system...Ch. 2 - For the rotational mechanical system with gears...Ch. 2 - For the rotational system shown in Figure P2.21,...Ch. 2 - Prob. 37PCh. 2 - Find the transfer function, Gs=4s/Ts , for the...Ch. 2 - For the rotational system shown in Figure P2.24,...Ch. 2 - Prob. 40PCh. 2 - Given the rotational system shown in Figure P226,...Ch. 2 - In the system shown in Figure P2.27, the inertia,...Ch. 2 - Prob. 43PCh. 2 - Given the combined translational and rotational...Ch. 2 - Prob. 45PCh. 2 - The motor whose torque-speed characteristics are...Ch. 2 - A dc motor develops 55 N-m of torque at a speed of...Ch. 2 - 48. In this chapter, we derived the transfer...Ch. 2 - Prob. 49PCh. 2 - Find the series and parallel analogs for the...Ch. 2 - Find the series and parallel analogs for the...Ch. 2 - A system’s output, c, is related to the system’s...Ch. 2 - Prob. 53PCh. 2 - Consider the differential equation...Ch. 2 - 55. Many systems are piecewise linear. That is,...Ch. 2 - For the translational mechanical system with a...Ch. 2 - 57. Enzymes are large proteins that biological...Ch. 2 - Prob. 58PCh. 2 - Figure P2.36 shows a crane hoisting a load....Ch. 2 - 60. In 1978, Malthus developed a model for human...Ch. 2 - 61. In order to design an underwater vehicle that...Ch. 2 - 62. The Gompertz growth model is commonly used to...Ch. 2 - A muscle hanging from a beam is shown in Figure...Ch. 2 - A three-phase ac/dc converter supplies dc to a...Ch. 2 - Prob. 65P
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- 38. Given the rotational system shown in Figure P2.24, find the transfer function, G(s) = 06(s)/01(s). [Section: 2.7]arrow_forwardJ 1. Using Lagrangian mechanics, derive the equations of motion of a cart with two tires under the cart shown in Figure P.4.1.arrow_forward2. A kilogram mass is attached to the end of the spring with spring constant 2 N/m. Find the equation of motion if the mass is initially released (set in motion) from rest from a point 1 meter above equilibrium position. (Use the convention that displacements measured below the equilibrium position are positive.) (a) Write the initial-value problem which describes the position of the mass. (b) Find the solution to your initial-value problem from part (a). (c) Graph the solution found in (b) on (0arrow_forward2. (25) For the rotational system shown in the fig- ure, write the equations of motion from which the transfer function, G(s) = 01(8)/T(s), can be found.arrow_forwardChapter 07, Problem 027 Z Your answer is partially correct. Try again. A spring and block are in the arrangement of the figure. When the block is pulled out to x = +4.0 cm, we must apply a force of magnitude 370N to hold it there. We pull the block to x = 11.0 cm and then release it. How much work does the spring do on the block when the block moves from x, = +5.0 cm to (a) x = +4.0 cm, (b) x = -4.0 cm, (c) x= -5.0 cm, and (d) x = -10.0 cm? x=0 Block F= 0 attached elleeee to spring (a) x positive F, negative (b) ugen/shared/assignment/test/aglist.uni?id=.. x negative 9:34 PM search A ENG 4/4/2021 ASUS 13) 1ghome f10 snd 17 4 7. 00 16 3.arrow_forwardE Q Figure P3.36 Three-phase AC system. 3-37. In a motion capture study of a runner, one frame shows the subject supporting her weight on one leg, as shown in Fig. P3.37. The length of the foot segment (from ankle to toe) is 8 in. and the length of the lower leg (from ankle to knee) is 18 in. X, in. (-6.25, 25) Ankle Introductory Mathematics for Engineering Applications 30 60⁰° y Knee X Toes (a) During a motion capture study. Knee Ankle Toes 0₁ -x, in. (b) To find ₁ and 0₂. Figure P3.37 Position of the runner's leg. a. Given the angles shown in Fig. P3.37(a), find the position of the knee if the runner's toes touch the ground at the point x = y = 0. b. Now suppose that the same leg is positioned such that the knee is located in the second quadrant and oriented in the knee-down position (clockwise direction), as shown Fig. P3.37(b). If the knee is located at P(x,y)=(−6.25 in.,25 in.), determine the values of 0₁ and 02. Pg. 88 Aa ☎( oooarrow_forward2.1 Figure P2.1 shows a single-mass translational mechanical system. Both springs are undeflected when z = 0 and fa(t) = o. Derive the mathematical model of the mechanical system. Figure P2.1 fa(t) www. Z m k₂ wwwarrow_forward1 An object of mass 125 kg is released from rest from a boat into the water and allowed to sink. While gravity is pulling the object down, a buoyancy force of times the weight of the object is pushing the object up (weight = mg). If we assume that water 40 resistance exerts a force on the object that is proportional to the velocity of the object, with proportionality constant 10 N-sec/m, find the equation of motion of the object. After how many seconds will the velocity of the object be 90 m/sec? Assume that the acceleration due to gravity is 9.81 m/ sec2. Find the equation of motion of the object. X(t) = %3Darrow_forwardFigure Q3 shows one cart with a mass that is separated from two walls by two springs and a dashpot, where kı, k2 and ka are the first, second spring and dashpot coefficients, respectively. The mass, m could represent an automobile system. An external force is also shown as F(t). Only horizontal motion and forces are considered. F(t) is input and x2(t) is output. (a) Derive all equations related to the system (b) Construct the block diagram from equation in (a) (c) Obtain the transfer function of the systemarrow_forwardll b) Obtain the mathematical model of the system shown in Figure Q2b using Newton's second law of motion, F=ma. k₁ w 3- 777777 C1 7771 k₂ D 7777 Figure: Q2b Page 2 of 7 A C2 1112arrow_forwardQ2. Figure Q2 shows a rotational mechanical system. Given J = 2 kg/m², J1 = 4 kg/m², K = 5 N-m/rad, D= 5 N-m-s/rad. (i) State the number of degrees of freedom of the system. Determine the equations of motion. (ii) (iii) Thus determine the transfer function T. D K Tm Om Ji Figure Q2arrow_forwardRotational Mechanical System: Find the transfer function for each rotational mechanicalnetwork shown belowarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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