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USING THE ENERGY METHOD, NOT EQUILIBRIUM.
Problems R, k1 Figure 346 Mechanical system.
3. The following figure shows the block diagram of a mechanical translational system k1 U3 m1...
3. The following figure shows the block diagram of a mechanical translational system k1 U3 m1 (a) Draw free body diagrams for each of the masses. Bearing in mind that the force due to spring is proportional to its length and the force due to friction is proportional to velocity, label each of the forces acting upon each body. (b) Develop the dynamical equations for the system.
Using the energy method, try to derive the equation of motion for system shown in the...
Using the energy method, try to derive the equation of motion for system shown in the Figure.
2. (15 scores) Consider the mechanical system shown in Figure 1. A spring exerts a force...
2. (15 scores) Consider the mechanical system shown in Figure 1. A spring exerts a force that is a function of its extension. A damper exerts a force that is a function of the velocity of the piston. Assume that the spring and the damper are both linear. (1) We want to describe the relation between the external force F(t) and the position yt) of the mass. Give the differential equation relating F(t) and y(t). Define this carefully as a...
17. Le Chatelier's Principle: pressure effects Consider the following system at equilibrium at 346 K: If...
17. Le Chatelier's Principle: pressure effects Consider the following system at equilibrium at 346 K: If the volume of the equilibrium system is suddenly increased at constant temperature: The reaction must: A. Run in the lorward direction to reestablish equiiorium B. Run in the reverse direction to reestablish equilibrium. C. Remain the same. Already at equilibrium. The number of moles of Br2 will: A. Increase. 8. Decrease. C. Remain the same. 18. Le Chatelier's Principle: mutiple etlects Consider the following...
Q5 The equation of the motion of the mechanical system shown in the following figure is...
Q5 The equation of the motion of the mechanical system shown in the following figure is governed by the following differential equation d2 x dx m7+9+= -f(t) - 3kx dt2 dt where m, C and k are mass, damping coefficient and spring constant, respectively. Consider the system with m = 10 kg, c = 80 Ns/m, k = 50 N/m, and the system is at rest at time t = 0 s. f(t) is the external force acting on the...
Rt)+ e(t) y(t) K1 S +4 Figure 3: A closed-loop control system with an inner feedback loop. Comput...
rt)+ e(t) y(t) K1 S +4 Figure 3: A closed-loop control system with an inner feedback loop. Compute the closed-loop transfer function Gal (s) -Y(s)/R(s) for the system shown in Figure 3
rt)+ e(t) y(t) K1 S +4 Figure 3: A closed-loop control system with an inner feedback loop. Compute the closed-loop transfer function Gal (s) -Y(s)/R(s) for the system shown in Figure 3
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...
Example 5a: Write, but do not solve the equations of motion for the mechanical network of Figure ...
translational
rotational
Example 5a: Write, but do not solve the equations of motion for the mechanical network of Figure 5a. 石 x20) K1 f(t) fv, Figure 5a 4/2019 ВЕКС 3533 Introduction to Control Systems Example 7: Write but do not solve, the Laplace transform of the equations of motion for the system shown in Figure 7. 6,(t) Di D2 D3 Figure 7 Example 8: Find the transfer function, θ2(s)/T(s), for the rotational mechanical system shown in Figure 8. 1 N-m/rad...
Problem 2: Transfer Functions of Mechanical Systems. (20 Points) A model sketch for a two-mass mechanical...
Problem 2: Transfer Functions of Mechanical Systems. (20 Points) A model sketch for a two-mass mechanical system subjected to fluctuations (t) at the wall is provided in figure 2. Spring k, is interconnected with both spring ka and damper Os at the nodal point. The independent displacement of mass m is denoted by 1, the independent displacement of mass m, is denoted by r2, and the independent displacement of the node is denoted by ra. Assume a linear force-displacement/velocity relationship...
Mechanical vibration subject 3. a. Consider the system of Figure 3. If C1 = C2 =...
Mechanical vibration subject
3. a. Consider the system of Figure 3. If C1 = C2 = C3 = 0, develops the equation of motion and predict the mass and stiffness matrices. Note that setting k3 = 0 in your solution should result in the stiffness matrix given by [ky + kz -k2 kz b. constructs the characteristics equation from Question 3(a) for the case m1 = 9 kg, m2 = 1 kg, k1 = 24 N/m, k2 = 3 N/m,...
3. The following figure shows the block diagram of a mechanical translational system k1 U3 m1 (a) Draw free body diagrams for each of the masses. Bearing in mind that the force due to spring is proportional to its length and the force due to friction is proportional to velocity, label each of the forces acting upon each body. (b) Develop the dynamical equations for the system.
Using the energy method, try to derive the equation of motion for system shown in the Figure.
2. (15 scores) Consider the mechanical system shown in Figure 1. A spring exerts a force that is a function of its extension. A damper exerts a force that is a function of the velocity of the piston. Assume that the spring and the damper are both linear. (1) We want to describe the relation between the external force F(t) and the position yt) of the mass. Give the differential equation relating F(t) and y(t). Define this carefully as a...
17. Le Chatelier's Principle: pressure effects Consider the following system at equilibrium at 346 K: If the volume of the equilibrium system is suddenly increased at constant temperature: The reaction must: A. Run in the lorward direction to reestablish equiiorium B. Run in the reverse direction to reestablish equilibrium. C. Remain the same. Already at equilibrium. The number of moles of Br2 will: A. Increase. 8. Decrease. C. Remain the same. 18. Le Chatelier's Principle: mutiple etlects Consider the following...
Q5 The equation of the motion of the mechanical system shown in the following figure is governed by the following differential equation d2 x dx m7+9+= -f(t) - 3kx dt2 dt where m, C and k are mass, damping coefficient and spring constant, respectively. Consider the system with m = 10 kg, c = 80 Ns/m, k = 50 N/m, and the system is at rest at time t = 0 s. f(t) is the external force acting on the...
rt)+ e(t) y(t) K1 S +4 Figure 3: A closed-loop control system with an inner feedback loop. Compute the closed-loop transfer function Gal (s) -Y(s)/R(s) for the system shown in Figure 3
rt)+ e(t) y(t) K1 S +4 Figure 3: A closed-loop control system with an inner feedback loop. Compute the closed-loop transfer function Gal (s) -Y(s)/R(s) for the system shown in Figure 3
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...
translational
rotational
Example 5a: Write, but do not solve the equations of motion for the mechanical network of Figure 5a. 石 x20) K1 f(t) fv, Figure 5a 4/2019 ВЕКС 3533 Introduction to Control Systems Example 7: Write but do not solve, the Laplace transform of the equations of motion for the system shown in Figure 7. 6,(t) Di D2 D3 Figure 7 Example 8: Find the transfer function, θ2(s)/T(s), for the rotational mechanical system shown in Figure 8. 1 N-m/rad...
Problem 2: Transfer Functions of Mechanical Systems. (20 Points) A model sketch for a two-mass mechanical system subjected to fluctuations (t) at the wall is provided in figure 2. Spring k, is interconnected with both spring ka and damper Os at the nodal point. The independent displacement of mass m is denoted by 1, the independent displacement of mass m, is denoted by r2, and the independent displacement of the node is denoted by ra. Assume a linear force-displacement/velocity relationship...
Mechanical vibration subject
3. a. Consider the system of Figure 3. If C1 = C2 = C3 = 0, develops the equation of motion and predict the mass and stiffness matrices. Note that setting k3 = 0 in your solution should result in the stiffness matrix given by [ky + kz -k2 kz b. constructs the characteristics equation from Question 3(a) for the case m1 = 9 kg, m2 = 1 kg, k1 = 24 N/m, k2 = 3 N/m,...
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