Concept explainers
Using the Routh table, tell how many poles of the following function are in the right half-plane. in the left hall-plane, and on the
Want to see the full answer?
Check out a sample textbook solutionChapter 6 Solutions
Control Systems Engineering
- Laplace transformationarrow_forwardThe one-dimensional harmonic oscillator has the Lagrangian L = mx˙2 − kx2/2. Suppose you did not know the solution of the motion, but realized that the motion must be periodic and therefore could be described by a Fourier series of the form x(t) =∑j=0 aj cos jωt, (taking t = 0 at a turning point) where ω is the (unknown) angular frequency of the motion. This representation for x(t) defines many_parameter path for the system point in configuration space. Consider the action integral I for two points t1 and t2 separated by the period T = 2π/ω. Show that with this form for the system path, I is an extremum for nonvanishing x only if aj = 0, for j ≠ 1, and only if ω2 = k/m.arrow_forwardnk int m The spring-mass-system shown in the figure has the following parameters: spring constant k = 4 N/m; mass m 6 %3D kg and the constant n = 1.6. M is the corresponding mass-matrix of the system. V1 and V2 are the eigenvectors associated with the smallest and largest natural frequencies of the system, respectively. If V,TV, = 1 and V2 V2 = 1, then what is value of V,™MV2 (in kg)? Answer:arrow_forward
- For the rotational mechanical system shown, find the transfer function Ɵ1(s)/T(s) and Ɵ2(s)/T(s).arrow_forwardNote: handwritten solutions are strictly prohibited...arrow_forwardConsider the following rotational mechanical system, a. Apply the "by inspection" method in Laplace domain to write the system of equations that represents the dynamics of the system b. Solve for the output variable q1(s). Use Cramer's rule or the substitution method to solve for the output variable q1(s). c. Give the transfer function G(s) = 91(s)/T(s) 0₁ (1) T(1) J1 82(1) oför J2 oooo K₁ K2 oooo Darrow_forward
- 7- In the two phase method if Max z* < 0 and at least one artificial vector appear in the optimum basic at a positive level (Aj 2 0). we proceed to phase -2.* true Falsearrow_forwardDerive the set of differential equations for a three mass-four sprang system as shown in Figure below that describes their time motion. Write the three differential equations in matrix form as figure attachment.arrow_forwardAll values equal to 1arrow_forward
- Obtain the Fourier series expansion for the following function 0arrow_forward4.78. Demonstrate that the system modes are orthogonal with respect to the [M] and [K] matrices for the following system: 10 0 0 (, 8-8 500 -50 X1 2 0 *2 + -50 400 -20 0 4 0 - 20 100 X3arrow_forward8arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY