θ3 02 12 Figure P4.28
ko θ2 Figure P4.34
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Eigenproblerm. 4.34. Consider the system shown in Figure P4.28. Let k63 = 0, Determine the equati...
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 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 potential energy and Lagrangian in terms of, and (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 shapes if m-30 g, 4-8 x...
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...
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...
Problem 5 (20%) For the system shown in Figure 5, a. How many degrees of freedom is this system and why? (5) b. If x3 0...
Problem 5 (20%) For the system shown in Figure 5, a. How many degrees of freedom is this system and why? (5) b. If x3 0 (the upper end is fixed and K1 and K2=K Write the equations of motion. Set the necessary matrix to find the natural frequencies and mode shapes (5) (5) (5) 1. 2. 3. Determine and explain how to get the natural frequencies. m2 Figure 5 www
Problem 5 (20%) For the system shown in Figure...
For a mass-spring system shown in the figure below. Write the dynamic equations in matrix form...
For a mass-spring system shown in the figure below. Write the dynamic equations in matrix form and find the natural frequencies for this system, eigen values, eigen vectors and mode shapes assuming: m1=1 kg, m2=4 kg, k1=k3=10 N/m, and k2=2 N/m. / ر2 دی) x1(0) x2(0) K3 K1 W K2 mi W4 m2 (-?
For the system shown in Figure 6, a. How many degrees of freedom is this system and why? b. Write the equations of moti...
For the system shown in Figure 6, a. How many degrees of freedom is this system and why? b. Write the equations of motion. For the remainder parts, assume alll the dampers are removed: c. If Ki=K3 and mim3, set the necessary matrix to find the natural frequencies and mode shapes d. For part c above, determine and explain how to get the natural frequencies. m1 Ty Absorber тз k1 С1 k3 m2 C2
For the system shown in Figure...
In the figure, the mass of the rigid rod Li is neglected while the beam L2...
In the figure, the mass of the rigid rod Li is neglected while the beam L2 has the mass m2. Define, a. The equations of motion b. The natural frequencies of the system mi Sk m2, ez (mı= 10 kg, mz= 48 kg, kl=2000 N/m, k2=5000 N/m, r=0.5 m, a=0.2 m, L=0.4 m, L2=0.6 m) Sk
Problem 3 (10 points). Consider the weakly coupled mechanical system shown in figure 2. Let are:...
Problem 3 (10 points). Consider the weakly coupled mechanical system shown in figure 2. Let are: k be the stiffness of the spring and mi-m2- m. Given that the initial conditions 1(0)0 6,(0)-A Oz(0)-0 02(0)0 I. Compute the complete solution of the system linearized around θ1 θ2 0 2. Given the numerical values in the following table, plot θ1(t) and θ2(t) on the same figure for 0 << 100s. Give a physical interpretation of what is happening Parameter Numerical Value...
i want to get part c,d The figure below is a gear-train mechanical system driven by...
i want to get part c,d
The figure below is a gear-train mechanical system driven by a prescribed motion in the form of an angular displacement y(t). The motion is caused by an applied torque T(t) generated by a motor. The mass moment of inertias of the motor and the driving gear are J and J, respectively, whereas the mass moment of inertias of the load and the driven gear are J, and J2, respectively. The radii and angular displacements...
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 potential energy and Lagrangian in terms of, and (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 shapes if m-30 g, 4-8 x...
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...
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...
Problem 5 (20%) For the system shown in Figure 5, a. How many degrees of freedom is this system and why? (5) b. If x3 0 (the upper end is fixed and K1 and K2=K Write the equations of motion. Set the necessary matrix to find the natural frequencies and mode shapes (5) (5) (5) 1. 2. 3. Determine and explain how to get the natural frequencies. m2 Figure 5 www
Problem 5 (20%) For the system shown in Figure...
For a mass-spring system shown in the figure below. Write the dynamic equations in matrix form and find the natural frequencies for this system, eigen values, eigen vectors and mode shapes assuming: m1=1 kg, m2=4 kg, k1=k3=10 N/m, and k2=2 N/m. / ر2 دی) x1(0) x2(0) K3 K1 W K2 mi W4 m2 (-?
For the system shown in Figure 6, a. How many degrees of freedom is this system and why? b. Write the equations of motion. For the remainder parts, assume alll the dampers are removed: c. If Ki=K3 and mim3, set the necessary matrix to find the natural frequencies and mode shapes d. For part c above, determine and explain how to get the natural frequencies. m1 Ty Absorber тз k1 С1 k3 m2 C2
For the system shown in Figure...
In the figure, the mass of the rigid rod Li is neglected while the beam L2 has the mass m2. Define, a. The equations of motion b. The natural frequencies of the system mi Sk m2, ez (mı= 10 kg, mz= 48 kg, kl=2000 N/m, k2=5000 N/m, r=0.5 m, a=0.2 m, L=0.4 m, L2=0.6 m) Sk
Problem 3 (10 points). Consider the weakly coupled mechanical system shown in figure 2. Let are: k be the stiffness of the spring and mi-m2- m. Given that the initial conditions 1(0)0 6,(0)-A Oz(0)-0 02(0)0 I. Compute the complete solution of the system linearized around θ1 θ2 0 2. Given the numerical values in the following table, plot θ1(t) and θ2(t) on the same figure for 0 << 100s. Give a physical interpretation of what is happening Parameter Numerical Value...
i want to get part c,d
The figure below is a gear-train mechanical system driven by a prescribed motion in the form of an angular displacement y(t). The motion is caused by an applied torque T(t) generated by a motor. The mass moment of inertias of the motor and the driving gear are J and J, respectively, whereas the mass moment of inertias of the load and the driven gear are J, and J2, respectively. The radii and angular displacements...
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