7. Consider the mechanical system shown below. The system initially at rest. The displacements u, y,...
Consider the mechanical system shown in Figure. Displacements Xi and Xo are measured from their respective equilibrium positions. Derive the transfer function of the system wherein Xi is the input and Xo is the output. Then obtain the response Xo (t) ki bi b,* when input Xi (t) is a step displacement of magnitude Xi occurring at t 0. Assume that Xo (0-) 0.
For the mechanical system shown below find the input-output equation relating xolt) to the displacement input x(t) 1. ド ド Ki Derive the transfer function X,G)/X, (s)of the mechanical system shown below. The displacements x, and xo are measured from their respective equilibrium potions. Is the system a first-order system if so, what is the time constant? 2. k1 bz k2 3. Consider the mechanical system shown below. The system is initially at rest. The displacements x, and x2 are...
02 Obtain the transfer function Y(s)yU(s) of the system shown in Figure. The vertical motion u at point P is the input. This system is a simplified version of an automobile or motorcycle suspension system. (In the figure mi and ki represent the wheel mass and tire stiffness, respectively.) Assume that the displacements x and y are measured from their respective equilibrium positions in the absence of the input u. Use Newton second law to derive the movement equations.
Problem B-4-1 Find the transfer function X (s)/X/(s) of the mechanical system shown in Figure 4-50. The displacements x; and X, are measured from their respective equilibrium positions. Obtain the displacement xo(t) when the input x;(t) is a step displacement of magnitude X; occurring at t = 0. Assume that x.(0-) = 0. T Figure 4-50 Mechanical system.
mi k2 b yi m2 Figure 5-45 Mechanical system. Assuming that mi 10 kg, m2 5 kg, b 10 N-s/m, k 40 N/m, and k 20 N/m and that input force u is a constant force of 5 N, obtain the response of the sys- tem. Plot the response curves n(t) versus r and y2(t) versus t with MATLAB Problem B-5-23 Consider the system shown in Figure 5-45. The system is at rest for t < 0. The dis placements...
10.Represent the translational mechanical system shown in the Figure in state- space, where xX3(t) is the output IN- 11.Find the state equations and output equation for the phase-variable representation of the transfer function G(s) 2s+1/(s2+7s+ 9) 12. Convert the state and output equations shown to a transfer function. -1.5 2 u(t) X = X 4 0 Y [1.5 0.625]x 13. For each system shown, write the state equations and the output equation for the phase- variable representation 8s10 sh25 t26...
Given a model of a mechanical system described by the following equation: sin(v)-cos(3)e-u Assume all initial conditions are at rest or equal to zero. (a) (20 pts) What is the state space representation of the model assuming the only output is angle v and single input is torque u? (b) (20 pts) What is the transfer function G(s) of the model for same single output and single input?
Question 3 (35 marks) Consider a mechanical system shown in Figure 3. The system is at rest for t<0. The input force f is applied at 0. The displacement x is the output of the system and is measured from the equilibrium position. kI b2 bi it Figure 3. Schematic of a mechanical system. (a) Obtain the traf) (10 marks) X (s) F(s) (b) Use of force-voltage analogy, obtain the equations for an electrical system (5 marks) (c) Draw a...
in the figure, obtain the state-space representation of the syster thè 1. Consider the mechanical system shown ssume y() is the output. (25 marks) ce representation of systel. ki lu k2
1.3. Assume a discrete-time system with input u(k) and output y(k). The system has a constant input disturbance d. Find the augmented state-space model with input Au(k) and output y(k) for the plant model given as below: Im(k +1) = AmIm (k) + Bmu(k) + Bad; y(k) = Cmlm (k) (1.82) [10.5 0 ] [ 0.51 where Am = 0.1 -0.1; Bm = 1 ; Cm = [101]; Ba= 100 0.8 -0.6 1. Calculate the plant transfer function that relates...