Consider the differential equation
Where f(x) is the input and is a function of the output, x. If
Want to see the full answer?
Check out a sample textbook solutionChapter 2 Solutions
Control Systems Engineering
- Find the local maximum and minimum values and saddle point(s) of the function. You are encouraged to use a calculator or computer to graph the function with a domain and viewpoint that reveals all the important aspects of the function. (Enter your answers as comma-separated lists. If an answer does not exist, enter DNE.) f(x, y) = 9 sin(x) sin(y), −? < x < ?, −? < y < ? local maximum value(s) local minimum value(s) saddle point(s) (x, y) =arrow_forwardLaplace transformationarrow_forwardPage 8/5 Q4: (M4) LE Velocity: V [km/hr] Wavelength: L [m] M k y(t) Model Height: H [m] The figure above shows a model of a person riding a unicycle that contains a spring under its seat. The spring constant is k = 10,600 N/m. Assume that damping is minimal, the wheel of the unicycle has no mass and is not a spring, the unicyle always stays perfectly upright, and the person is represented by a rigid mass M = kg. a) When the unicycle is being ridden at speed V = 10 km/hr over the sinusoidal bumpy terrain shown above, with bump spacing L=0.6 m and bump height H 0.05 m, what will be the steady-state peak-to-peak amplitude of the motion y(t) [m] of the person riding the unicycle? b) Recalculate the steady-state peak-to-peak amplitude of the motion for 2.5, 5, and 20 km/hr. Will the rider have difficulty reaching speeds above 5 km/hr?arrow_forward
- 2. In the following electrical circuit system, where R is the resistance, L is the inductance, and C is the capacitance. The input variable is the applied voltage the output variable is the voltage Find the transfer function of the 11 L ic İR OR 10arrow_forwardHarmonic oscillators. One of the simplest yet most important second-order, linear, constant- coefficient differential equations is the equation for a harmonic oscilator. This equation models the motion of a mass attached to a spring. The spring is attached to a vertical wall and the mass is allowed to slide along a horizontal track. We let z denote the displacement of the mass from its natural resting place (with x > 0 if the spring is stretched and x 0 is the damping constant, and k> 0 is the spring constant. Newton's law states that the force acting on the oscillator is equal to mass times acceleration. Therefore the differential equation for the damped harmonic oscillator is mx" + bx' + kr = 0. (1) k Lui Assume the mass m = 1. (a) Transform Equation (1) into a system of first-order equations. (b) For which values of k, b does this system have complex eigenvalues? Repeated eigenvalues? Real and distinct eigenvalues? (c) Find the general solution of this system in each case. (d)…arrow_forward1. Find the transfer function. A = [² = ₁], B = [1] . C = [0_1], D = F2] SEST-AT Y(s) U(s) = C[sl-A] B+D X = AY + Bui V = Cx + Duarrow_forward
- O 1::09 O [Template] Ho... -> Homework For the system shown in figure below, Find the range of K for stable system. R K(s + 2) C s(s +5)(s² + 2s + 5) IIarrow_forward3 5. `x, X, -3 6 [3 0 0 6 6 Determine the steady-state respanse et the System given above.arrow_forwardFor the mechanical translation system below, find the force-voltage analogy and force-current analogy. Use the following values. K1 = 2 fv, = 1/2 M1 = 1+a %3D K2 = 2 fv2 = 4+b M2 = 5 K3 = 3+c fv3 = 3 a = 0 where a = 3rd digit of your student number %3D b = 5th digit of your student number b =7 C = 7th digit of your student number C = 5 For reference, the 1st digit of your student number is the leftmost number in your student number. Indicate your student number when solving problems.arrow_forward
- nk 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_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_forwardFor the mechanical translation system below, find the transfer function 0,/T and O2/T. Use the following values. K = 1+c D1 = 1 Jj = 4+a J2 = 3+b D2 = 5 where a = 3rd digit of your student number %3D = 7 = 5 b = 5th digit of your student number c = 7th digit of your student number For reference, the 1st digit of your student number is the leftmost number in your student number. Indicate your student number when solving problems. T(t) 0(t) 02(1), elel J2 D1 K D2 ON II ||||arrow_forward
- 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