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Consider the mechanical system shown in Figure. Displacements Xi and Xo are measured from their respective...
Problem B-4-1 Find the transfer function X (s)/X/(s) of the mechanical system shown in Figure 4-50....
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.
Question 3 (35 marks) Consider a mechanical system shown in Figure 3. The system is at rest for t
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...
7. Consider the mechanical system shown below. The system initially at rest. The displacements u, y,...
7. Consider the mechanical system shown below. The system initially at rest. The displacements u, y, and z are measured from their respective rest positions. Given that u is the input, y is the output, 1) Obtain the transfer function of the system (20pt). 2) Obtain a state-space representation of the system (20pt). I b, - obteranlara k, 12 WI
For the mechanical system shown below find the input-output equation relating xolt) to the displacement input...
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...
B-3-7. Obtain the XO (s)/ Xi (s) transfer function from each of the 3 mechanical systems in Figure 3-54. In the diagram...
B-3-7. Obtain the XO (s)/ Xi (s) transfer function from each of the 3 mechanical systems in Figure 3-54. In the diagrams, xi represents the displacement and x0 denotes the departure displacement (each displacement is measured from from its equilibrium position INGENIERIA DE CONTROL MODERNA Figura 3-54 Sistemas mecánicos
B-3-7. Obtain the XO (s)/ Xi (s) transfer function from each of the 3 mechanical systems in Figure 3-54. In the diagrams, xi represents the displacement and x0 denotes the departure...
02 Obtain the transfer function Y(s)yU(s) of the system shown in Figure. The vertical motion u...
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.
2. A two-mass translational mechanical system has the following mathematical model: mž +bi,+k, (*; - x)=f,0)...
2. A two-mass translational mechanical system has the following mathematical model: mž +bi,+k, (*; - x)=f,0) m,ž, +b,X, +k, (x2 – x)+k,x, = 0 The displacements Xi and X2 are measured from their respective equilibrium positions. An external force falt) is applied to the system. Sketch a possible configuration of the two-mass mechanical system. Label all elements and show the positive convention for displacement in your sketch. (Hint verify the system model by applying Newton's laws.)
For the lever system shown, the input to the system is the displacement, y, and the...
For the lever system shown, the input to the system is the displacement, y, and the angle θ is the output. The position θ 0 corresponds to the equilibrium position when y-0. The lever has an inertia I about the pivot. Assume small displacements. 3. ki Derive the equation of motion Find the transfer function for the system. Discuss whether or not this system has numerator dynamics and what affect this has on the response Use the tf and impulse...
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/...
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...
Q2 A rotational mechanical system is shown in Figure 2.1. T(t) is the external torque and...
Q2 A rotational mechanical system is shown in Figure 2.1. T(t) is the external torque and is the input to the system. 01(t) is the angular displacement of inertia Ji and O2(t) is the angular displacement of inertia J2. C and C are friction coefficients and K, and K2 are spring constants. (a) Draw the free-body diagrams for J; and Jz. (7 marks) (b) Derive the equations of motion for the system shown in Figure 2.1. (8 marks) (c) Using...
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.
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...
7. Consider the mechanical system shown below. The system initially at rest. The displacements u, y, and z are measured from their respective rest positions. Given that u is the input, y is the output, 1) Obtain the transfer function of the system (20pt). 2) Obtain a state-space representation of the system (20pt). I b, - obteranlara k, 12 WI
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...
B-3-7. Obtain the XO (s)/ Xi (s) transfer function from each of the 3 mechanical systems in Figure 3-54. In the diagrams, xi represents the displacement and x0 denotes the departure displacement (each displacement is measured from from its equilibrium position INGENIERIA DE CONTROL MODERNA Figura 3-54 Sistemas mecánicos
B-3-7. Obtain the XO (s)/ Xi (s) transfer function from each of the 3 mechanical systems in Figure 3-54. In the diagrams, xi represents the displacement and x0 denotes the departure...
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.
2. A two-mass translational mechanical system has the following mathematical model: mž +bi,+k, (*; - x)=f,0) m,ž, +b,X, +k, (x2 – x)+k,x, = 0 The displacements Xi and X2 are measured from their respective equilibrium positions. An external force falt) is applied to the system. Sketch a possible configuration of the two-mass mechanical system. Label all elements and show the positive convention for displacement in your sketch. (Hint verify the system model by applying Newton's laws.)
For the lever system shown, the input to the system is the displacement, y, and the angle θ is the output. The position θ 0 corresponds to the equilibrium position when y-0. The lever has an inertia I about the pivot. Assume small displacements. 3. ki Derive the equation of motion Find the transfer function for the system. Discuss whether or not this system has numerator dynamics and what affect this has on the response Use the tf and impulse...
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...
Q2 A rotational mechanical system is shown in Figure 2.1. T(t) is the external torque and is the input to the system. 01(t) is the angular displacement of inertia Ji and O2(t) is the angular displacement of inertia J2. C and C are friction coefficients and K, and K2 are spring constants. (a) Draw the free-body diagrams for J; and Jz. (7 marks) (b) Derive the equations of motion for the system shown in Figure 2.1. (8 marks) (c) Using...
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