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Problem 3: The system in Figure 3 consists of a double pendulum where both masses are...
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...
MatLab work preferred, but please show/describe process. I) 3-DOF Pendulum System Using matrix algebra, analyze the...
MatLab work preferred, but please show/describe process.
I) 3-DOF Pendulum System Using matrix algebra, analyze the vibration of following 3-DOF pendulum system. Where, a is the distance from the pivot point to the spring, and L is the length of the pendulum string. Derive: the equations of motion, the system natural frequencies and system's mode shapes 01 02 K2 mi m2 m3 Data: mi 5 kg m2 = 5 kg m3 5 kg k1 100 N/m k2 100 N/m L...
A2. Two identical simple pendulums are connected via a spring as it is shown in Figure A2. The length of the pendulum strut L-0.5m and the mass of attached bob m-2kg, the stiffness coefficient of the...
A2. Two identical simple pendulums are connected via a spring as it is shown in Figure A2. The length of the pendulum strut L-0.5m and the mass of attached bob m-2kg, the stiffness coefficient of the connecting spring is k-80Ns/m. 02 Figure A2. a) Using the free-body diagram method derive the following governing equations for the coupled pendulum system which are given below in matrix form b) Using the characteristic equation method or transformation to principal coordinates find out two...
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...
(3) (20 points) The (dimensionless) equations of motion for a frictionless double pendulum system...
please use mathematica for code NOT MATLAB
(3) (20 points) The (dimensionless) equations of motion for a frictionless double pendulum system as shown below (in the figure on the left) with mi m2 and L1 L are The solutions are graphed below (on the right) for the initial conditions θι (0) 2, θ1(0) 1.02(0) 0, and 02(0)-0 for oS t s 50. (a) Reformulate the IVP as a first order system.2 (b) Generate approximate solutions using any method (Euler, improved...
Problem 1: The system in Figure 1 comprises two masses connected to one another through a...
Problem 1: The system in Figure 1 comprises two masses connected to one another through a spring. The block slides without friction on the support and has mass mi. The disk has radius a, mass moment of inertia I, and mass m2. The disk rolls without slipping on the support. The springs are unstretched when x(t) = x2(t) = 0. 2k 3k , m Figure 1: System for Problem 1 (a) Derive the differential equations of motion for the system...
. Consider the Furuta pendulum system; See Figure1 on the next page. The angle of the...
. Consider the Furuta pendulum system; See Figure1 on the next page. The angle of the horizontal arm is denoted θ1 and the angle of the pendulum fron the vertically upward line is denoted θ2. Their corresponding angular velocities are denoted θ| and 02, respectively. The kinetic energy K and the potential energy V of the system are given by Vo COS in terms of some mechanical parameters Io, 111, 12, 112, Vo of the system that have all positive...
Homework 7: Undamped, 2-DOF System 1. A system with two masses of which the origins are...
Homework 7: Undamped, 2-DOF System 1. A system with two masses of which the origins are at the SEPs is shown in Figure 1. The mass of m2 is acted by the external force of f(t). Assume that the cable between the two springs, k2 and k3 is not stretchable. Solve the following problems (a) Draw free-body diagrams for the two masses and derive their EOMs (b) Represent the EOMs in a matrix fornm (c) Find the undamped, natural frequencies...
applied to the masesdthe displacements I1 and sg of the mases For the system in Figure...
applied to the masesdthe displacements I1 and sg of the mases For the system in Figure 5.49, the inputs are the forcesfi and f2 applied to the masses and the outputs are the displacements x and x2 of the masses a. Draw the necessary free-body diagrams and derive the differential equations of motion b. Write the differential equations of motion in the second-order matrix form. c. Using the differential equations obtained in Part (a), determine the state-space representation 15. Repeat...
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...
MatLab work preferred, but please show/describe process.
I) 3-DOF Pendulum System Using matrix algebra, analyze the vibration of following 3-DOF pendulum system. Where, a is the distance from the pivot point to the spring, and L is the length of the pendulum string. Derive: the equations of motion, the system natural frequencies and system's mode shapes 01 02 K2 mi m2 m3 Data: mi 5 kg m2 = 5 kg m3 5 kg k1 100 N/m k2 100 N/m L...
A2. Two identical simple pendulums are connected via a spring as it is shown in Figure A2. The length of the pendulum strut L-0.5m and the mass of attached bob m-2kg, the stiffness coefficient of the connecting spring is k-80Ns/m. 02 Figure A2. a) Using the free-body diagram method derive the following governing equations for the coupled pendulum system which are given below in matrix form b) Using the characteristic equation method or transformation to principal coordinates find out two...
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...
please use mathematica for code NOT MATLAB
(3) (20 points) The (dimensionless) equations of motion for a frictionless double pendulum system as shown below (in the figure on the left) with mi m2 and L1 L are The solutions are graphed below (on the right) for the initial conditions θι (0) 2, θ1(0) 1.02(0) 0, and 02(0)-0 for oS t s 50. (a) Reformulate the IVP as a first order system.2 (b) Generate approximate solutions using any method (Euler, improved...
Problem 1: The system in Figure 1 comprises two masses connected to one another through a spring. The block slides without friction on the support and has mass mi. The disk has radius a, mass moment of inertia I, and mass m2. The disk rolls without slipping on the support. The springs are unstretched when x(t) = x2(t) = 0. 2k 3k , m Figure 1: System for Problem 1 (a) Derive the differential equations of motion for the system...
. Consider the Furuta pendulum system; See Figure1 on the next page. The angle of the horizontal arm is denoted θ1 and the angle of the pendulum fron the vertically upward line is denoted θ2. Their corresponding angular velocities are denoted θ| and 02, respectively. The kinetic energy K and the potential energy V of the system are given by Vo COS in terms of some mechanical parameters Io, 111, 12, 112, Vo of the system that have all positive...
Homework 7: Undamped, 2-DOF System 1. A system with two masses of which the origins are at the SEPs is shown in Figure 1. The mass of m2 is acted by the external force of f(t). Assume that the cable between the two springs, k2 and k3 is not stretchable. Solve the following problems (a) Draw free-body diagrams for the two masses and derive their EOMs (b) Represent the EOMs in a matrix fornm (c) Find the undamped, natural frequencies...
applied to the masesdthe displacements I1 and sg of the mases For the system in Figure 5.49, the inputs are the forcesfi and f2 applied to the masses and the outputs are the displacements x and x2 of the masses a. Draw the necessary free-body diagrams and derive the differential equations of motion b. Write the differential equations of motion in the second-order matrix form. c. Using the differential equations obtained in Part (a), determine the state-space representation 15. Repeat...
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