Engineering Your Future: Comprehensive
8th Edition
ISBN: 9780199348015
Author: William C. Oakes, Les L. Leone
Publisher: Oxford University Press
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Chapter 2, Problem 2.42EAA
To determine
One field of engineering and write a one-page paper on how the advances in information technology have influenced that field.
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##### For the attached electropneumatic circuit, design where and how a counter should be attached so that a part is counted for each cycle
If you have a spring mass damper system, given by m*x_double_dot + c*x_dot + kx = 0 where m, c, k (all positive scalars) are the mass, damper coefficient, and spring coefficient, respectively. x ∈ R represents the displacement of the mass.
Let us then discuss the stability of the system by using Lyapunov stability theorem. Consider the system energy as a candidate Lyapunov function shown in the image.
Discuss the positive definiteness of V (x, x_dot).
Derive the Lyapunov rate of this system (i.e., V_dot ), and discuss the stability property of thesystem based on the information we gain from ̇V_dot .
In class, two approaches—Theorems 1 and 2 below—are discussed to prove asymptotic stability of asystem when ̇V = 0.
Show the asymptotic stability of the system given in Eq. (1) by applying Theorem 1.
Show the asymptotic stability of the system given in Eq. (1) by applying Theorem 2.
Chapter 2 Solutions
Engineering Your Future: Comprehensive
Ch. 2 - Prob. 2.1EAACh. 2 - Prob. 2.2EAACh. 2 - Prob. 2.3EAACh. 2 - Prob. 2.4EAACh. 2 - Prob. 2.5EAACh. 2 - Prob. 2.6EAACh. 2 - Prob. 2.7EAACh. 2 - Prob. 2.8EAACh. 2 - Prob. 2.9EAACh. 2 - Prob. 2.10EAA
Ch. 2 - Prob. 2.11EAACh. 2 - Prob. 2.12EAACh. 2 - Prob. 2.13EAACh. 2 - Prob. 2.14EAACh. 2 - Prob. 2.15EAACh. 2 - Prob. 2.16EAACh. 2 - Prob. 2.17EAACh. 2 - Prob. 2.18EAACh. 2 - Prob. 2.19EAACh. 2 - Prob. 2.20EAACh. 2 - Prob. 2.21EAACh. 2 - Prob. 2.22EAACh. 2 - Prob. 2.23EAACh. 2 - Prob. 2.24EAACh. 2 - Prob. 2.25EAACh. 2 - Prob. 2.26EAACh. 2 - Prob. 2.27EAACh. 2 - Prob. 2.28EAACh. 2 - Prob. 2.29EAACh. 2 - Prob. 2.30EAACh. 2 - Prob. 2.31EAACh. 2 - Prob. 2.32EAACh. 2 - Prob. 2.33EAACh. 2 - Prob. 2.34EAACh. 2 - Prob. 2.35EAACh. 2 - Prob. 2.36EAACh. 2 - Prob. 2.37EAACh. 2 - Prob. 2.38EAACh. 2 - Prob. 2.39EAACh. 2 - Prob. 2.40EAACh. 2 - Prob. 2.41EAACh. 2 - Prob. 2.42EAACh. 2 - Prob. 2.43EAACh. 2 - Prob. 2.44EAACh. 2 - Prob. 2.45EAACh. 2 - Prob. 2.46EAACh. 2 - Prob. 2.47EAACh. 2 - Prob. 2.48EAACh. 2 - Prob. 2.49EAACh. 2 - Prob. 2.50EAA
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- Homework#5arrow_forwardIf you have a spring mass damper system, given by m*x_double_dot + c*x_dot + kx = 0 where m, c, k (all positive scalars) are the mass, damper coefficient, and spring coefficient, respectively. x ∈ R represents the displacement of the mass. Using linear stability analysis, show that the system is asymptotically stable. Hint: stability of a linear system z_dot = Az is characterized by the eigenvalues of A.arrow_forwardWhat would the electropneumatic diagram of a circuit with the sequence a+b+c+(a-b-c-) look like?arrow_forward
- ### What would the electropneumatic diagram of a circuit with the sequence a+b+c+(a-b-c-) look like, with a counter, in the fluidsim?arrow_forwardYou are asked to design a unit to condense ammonia. The required condensation rate is 0.09kg/s. Saturated ammonia at 30 o C is passed over a vertical plate (10 cm high and 25 cm wide).The properties of ammonia at the saturation temperature of 30°C are hfg = 1144 ́10^3 J/kg andrv = 9.055 kg/m 3 . Use the properties of liquid ammonia at the film temperature of 20°C (Ts =10 o C):Pr = 1.463 rho_l= 610.2 kf/m^3 liquid viscosity= 1.519*10^-4 kg/ ms kinematic viscosity= 2.489*10^-7 m^2/s Cpl= 4745 J/kg C kl=0.4927 W/m CCalculate the surface temperature required to achieve the desired condensation rate of 0.09 kg/s( should be 688 degrees C) a) Show that if you use a bigger vertical plate (2.5 m-wide and 0.8 m-height), the requiredsurface temperature would be now 20 o C. You may use all the properties given as an initialguess. No need to iterate to correct for Tf. b) What if you still want to use small plates because of the space constrains? One way to getaround this problem is to use small…arrow_forwardHomework#5arrow_forward
- Question 1: Beam Analysis Two beams (ABC and CD) are connected using a pin immediately to the left of Point C. The pin acts as a moment release, i.e. no moments are transferred through this pinned connection. Shear forces can be transferred through the pinned connection. Beam ABC has a pinned support at point A and a roller support at Point C. Beam CD has a roller support at Point D. A concentrated load, P, is applied to the mid span of beam CD, and acts at an angle as shown below. Two concentrated moments, MB and Mc act in the directions shown at Point B and Point C respectively. The magnitude of these moments is PL. Moment Release A B с ° MB = PL Mc= = PL -L/2- -L/2- → P D Figure 1: Two beam arrangement for question 1. To analyse this structure, you will: a) Construct the free body diagrams for the structure shown above. When constructing your FBD's you must make section cuts at point B and C. You can represent the structure as three separate beams. Following this, construct the…arrow_forwardA differential element on the bracket is subjected to plane strain that has the following components:, Ɛx = 300 × 10-6, Ɛy = 150 × 10-6, Ɛxy = -750 x 10-6. Use the strain-transformation equations and determine the normal strain Ɛx in the X/ direction on an element oriented at an angle of 0 = 40°. Note, a positive angle, 0, is counter clockwise. x Enter your answer in micro strain to a precision of two decimal places. eg. if your answer is 300.15X106, please enter 300.15.arrow_forwardIf the 50 mm diameter shaft is made from brittle material having an ultimate strength of σult=595 MPa for both tension and compression, determine the factor of safety of the shaft against rupture. The applied force, F, is 140 kN. The applied torque T, is 5.0 kN⚫m. Enter your answer to a precision of two decimal places. T Farrow_forward
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