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Q3. For the system in Figure 3 where and θ2 are the rotational angles, and are the rotary inertias of the two disks with radius r and 2r, respectively, 2r (1) Find its total kinetic energy, total pot...
Q3. For the system in Figure 3 where 0 and angles, and are the rotary inertias of the two disks with are the rotati...
Q3. For the system in Figure 3 where 0 and angles, and are the rotary inertias of the two disks with are the rotational radius r and 2r, respectively, 2r (1) Find its total kinetic energy, total potential energy and Lagrangian in terms of 0, and 0 (2) Derive the equations of motion using Lagrangian equation method (3) Put the equations of motion in matrix form, and (4) Calculate the natural frequencies and the associated mode Fosin shapes if m...
03. For the system in Figure 3 where and are the rotational angles, /, and 2 are the rotary inertias of the two disks w...
03. For the system in Figure 3 where and are the rotational angles, /, and 2 are the rotary inertias of the two disks with radius r and 2r, respectively, (1) Find its total kinetic energy, total potential energy and e, 2r Lagrangian in terms of θ' and θ, (2) Derive the equations of motion using Lagrangian equation method (3) Put the equations of motion in matrix form, and Im In 4) Calculate the natural frequencies and the associated mode...
Q3. For the rotational system subjected to an applied torque Mocosout shown in Figure 3, the...
Q3. For the rotational system subjected to an applied torque Mocosout shown in Figure 3, the rotary inertia of the rigid bar about the hinge O can be calculated by Jo =7ml /48. Given k = 5,000N/m, 1 - 1m, m = 20 kg, Mo = 100 Nm, c = 130 rpm. Assume rotation angle is very small, (i) Draw the free body diagram; (ii) Use Newton's 2nd law to derive the equation of motion of the system; and (iii)...
Problem 3: The system in Figure 3 consists of a double pendulum where both masses are...
Problem 3: The system in Figure 3 consists of a double pendulum where both masses are m and both lengths are L 2 Figure 3: System for Problem 3 (a) Derive the differential equations of motion for the system. The angles a(t) and θ2(t) can be arbitrarily large. (b) Linearize the equations by assuming that a (t) and 02(t) are small. Write the linearized differential equations in matrix form (c) Obtain the natural frequencies and modes of vibration. (d) Plot...
1 Q2. Figure 2 shows a system in which mass m is connected with a cylinder of mass m2 and moment of inertia Jo through...
1 Q2. Figure 2 shows a system in which mass m is connected with a cylinder of mass m2 and moment of inertia Jo through a horizontal spring k. The cylinder is m1 rolling on the rough surface without slipping. (1) Find its total kinetic energy, total potential energy TN and Lagrangian, Figure 2 (2) Derive the equations of motion using Lagrangian equation method, and (3) Calculate its natural frequencies
1 Q2. Figure 2 shows a system in which mass...
Q4. For the system shown in Figure 4 where m=10 kg, 100 kN/m, the governing equations has been derived as (1) Find the...
Q4. For the system shown in Figure 4 where m=10 kg, 100 kN/m, the governing equations has been derived as (1) Find the natural frequencies of the system; (2) Determine the associated mode shapes; and (3) Obtain the vibration response if the initial conditions are given as x,(0)-0,x,(0)-0.001 m, 2E 2m 1n Figure 4
Q4. For the system shown in Figure 4 where m=10 kg, 100 kN/m, the governing equations has been derived as (1) Find the natural frequencies of...
Q4. For the systern shown in Figure 4 where m=10 kg, k = 100 kN/m, the governing equations has been derived as (1) Find...
Q4. For the systern shown in Figure 4 where m=10 kg, k = 100 kN/m, the governing equations has been derived as (1) Find the natural frequencies of the system; (2) Determine the associated mode shapes; and (3) Obtain the vibration response if the initial conditions are given as x (0) 0, x, (0) 0.001 m 2k E 2m Figure 4
Q4. For the systern shown in Figure 4 where m=10 kg, k = 100 kN/m, the governing equations has...
Solve a,b and c The vibratory movement of the engineering system shown in Figure 3 can...
Solve a,b and c
The vibratory movement of the engineering system shown in Figure 3 can be described by two generalised coordinates, x, a Cartesian coordinate, and 6, a polar coordinate systems. The mass m and its mass moment of inertia about an axis that goes through its centre of gravity G is J. When the system is slightly pushed down from the top comer at the right hand edge of mass m, the induced vibrational motion is found to...
For the system shown in Fig. 1, solve the following problems. (a) Find the transfer function, G(s...
For the system shown in Fig. 1, solve the following problems. (a) Find the transfer function, G(s)X2 (s)/F(s) (b) Does the system oscillate with a unit step input (f (t))? Explain the reason (c) Decide if the system(x2 (t)) is stable with a unit step input (f (t))? Explain the reason 1. 320) 8 kg 2 N/m 4N-s/m 2N-s/m Fig. 1 2. There are two suspensions for a car as shown in Fig. 2 (a) Find the equations of each...
Q3. For the system in Figure 3 where 0 and angles, and are the rotary inertias of the two disks with are the rotational radius r and 2r, respectively, 2r (1) Find its total kinetic energy, total potential energy and Lagrangian in terms of 0, and 0 (2) Derive the equations of motion using Lagrangian equation method (3) Put the equations of motion in matrix form, and (4) Calculate the natural frequencies and the associated mode Fosin shapes if m...
03. For the system in Figure 3 where and are the rotational angles, /, and 2 are the rotary inertias of the two disks with radius r and 2r, respectively, (1) Find its total kinetic energy, total potential energy and e, 2r Lagrangian in terms of θ' and θ, (2) Derive the equations of motion using Lagrangian equation method (3) Put the equations of motion in matrix form, and Im In 4) Calculate the natural frequencies and the associated mode...
Q3. For the rotational system subjected to an applied torque Mocosout shown in Figure 3, the rotary inertia of the rigid bar about the hinge O can be calculated by Jo =7ml /48. Given k = 5,000N/m, 1 - 1m, m = 20 kg, Mo = 100 Nm, c = 130 rpm. Assume rotation angle is very small, (i) Draw the free body diagram; (ii) Use Newton's 2nd law to derive the equation of motion of the system; and (iii)...
Problem 3: The system in Figure 3 consists of a double pendulum where both masses are m and both lengths are L 2 Figure 3: System for Problem 3 (a) Derive the differential equations of motion for the system. The angles a(t) and θ2(t) can be arbitrarily large. (b) Linearize the equations by assuming that a (t) and 02(t) are small. Write the linearized differential equations in matrix form (c) Obtain the natural frequencies and modes of vibration. (d) Plot...
1 Q2. Figure 2 shows a system in which mass m is connected with a cylinder of mass m2 and moment of inertia Jo through a horizontal spring k. The cylinder is m1 rolling on the rough surface without slipping. (1) Find its total kinetic energy, total potential energy TN and Lagrangian, Figure 2 (2) Derive the equations of motion using Lagrangian equation method, and (3) Calculate its natural frequencies
1 Q2. Figure 2 shows a system in which mass...
Q4. For the system shown in Figure 4 where m=10 kg, 100 kN/m, the governing equations has been derived as (1) Find the natural frequencies of the system; (2) Determine the associated mode shapes; and (3) Obtain the vibration response if the initial conditions are given as x,(0)-0,x,(0)-0.001 m, 2E 2m 1n Figure 4
Q4. For the system shown in Figure 4 where m=10 kg, 100 kN/m, the governing equations has been derived as (1) Find the natural frequencies of...
Q4. For the systern shown in Figure 4 where m=10 kg, k = 100 kN/m, the governing equations has been derived as (1) Find the natural frequencies of the system; (2) Determine the associated mode shapes; and (3) Obtain the vibration response if the initial conditions are given as x (0) 0, x, (0) 0.001 m 2k E 2m Figure 4
Q4. For the systern shown in Figure 4 where m=10 kg, k = 100 kN/m, the governing equations has...
Solve a,b and c
The vibratory movement of the engineering system shown in Figure 3 can be described by two generalised coordinates, x, a Cartesian coordinate, and 6, a polar coordinate systems. The mass m and its mass moment of inertia about an axis that goes through its centre of gravity G is J. When the system is slightly pushed down from the top comer at the right hand edge of mass m, the induced vibrational motion is found to...
For the system shown in Fig. 1, solve the following problems. (a) Find the transfer function, G(s)X2 (s)/F(s) (b) Does the system oscillate with a unit step input (f (t))? Explain the reason (c) Decide if the system(x2 (t)) is stable with a unit step input (f (t))? Explain the reason 1. 320) 8 kg 2 N/m 4N-s/m 2N-s/m Fig. 1 2. There are two suspensions for a car as shown in Fig. 2 (a) Find the equations of each...
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