![Consider an undamped system where the vector-matrix form of the system model is: Mx+Kx = ft) 90 F(1) M= [ ] K = 5220 -1440 L-](http://img.homeworklib.com/questions/79d31db0-fa18-11ea-ae6d-470bdfcca2d3.png?x-oss-process=image/resize,w_560)
Homework Answers
![2 x,Tmx, = 1 10+ [ 12:31: Chic 1.1 1.125] [3] 2 Bi ( 9 +5.0625)= 1 B, = 0.2667. To-2661 . X, 0.3 >2=900 1440X2=0 (5220 - 9x](http://img.homeworklib.com/questions/7b20ecd0-fa18-11ea-96df-1d3be8311b85.png?x-oss-process=image/resize,w_560)
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Consider an undamped system where the vector-matrix form of the system model is: Mx+Kx = ft)...
Consider an undamped system where the vector-matrix form of the system model is: F(t) [8 olx...
Consider an undamped system where the vector-matrix form of the system model is: F(t) [8 olx Mx + Kx = 0 18X, + 2000 -1800 x -1800 4500 I:1-[0] The system is initially at rest with x(0) = 0 and x,0)=0 when input F(t) = 84 sin15t is applied to the system. Use the modal decomposition method described in chapter 5 to find the system response. Some intermediate results (find these as part of your solution) are: The system's two...
Consider an undamped system where the vector-matrix form of the system model is: [F(t) [8 orë...
Consider an undamped system where the vector-matrix form of the system model is: [F(t) [8 orë Mx + x = LO 183, 2000 -1800 x (-1800 45001 The system is initially at rest with X (0) = 0 and 2,0)=0 when input F(t) = 84 sin 15t is applied to the system. Use the modal decomposition method described in chapter 5 to find the system response. Some intermediate results (find these as part of your solution) are: The system's two...
The vector-matrix form of the system model is: (18 0 18000 72001 x f(t) or Mx...
The vector-matrix form of the system model is: (18 0 18000 72001 x f(t) or Mx + Kx = f(t) 08.3. -7200 8000 | X, 3. (1) X= M = (18 0 08 K 18000 -7200 7200 8000 and f(t) = (1) 12(0)] [x₂(t) The system's eigenvalues, natural frequencies, and eigenvectors are: 1 2 = 400, 0, = 20 s', and v, 1.5 1.) = 1600, 0), = 40 s', and v, = -1.5 1 1 The inverse of modal...
Consider an undamped system where the vector-matrix form of the system model is: [F(t) [18 07ž...
Consider an undamped system where the vector-matrix form of the system model is: [F(t) [18 07ž Mx + Kx = 083, + [18000 -72007x -7200 8000X, E]-[] The input to the system is F(t) = 6300 sin (30t). Use modal decomposition to find the system's frequency response. Note that the frequency response is the particular solution, and also called the steady-state response.
The vector-matrix form of the system model is: (18 0 18000 72001 x f(t) or Mx...
The vector-matrix form of the system model is: (18 0 18000 72001 x f(t) or Mx + Kx = f(t) 08.3. -7200 8000 | X, 3. (1) X= M = (18 0 08 K 18000 -7200 7200 8000 and f(t) = (1) 12(0)] [x₂(t) The system's eigenvalues, natural frequencies, and eigenvectors are: 1 2 = 400, 0, = 20 s', and v, 1.5 1.) = 1600, 0), = 40 s', and v, = -1.5 1 1 The inverse of modal...
Consider an undamped system where the vector-matrix form of the system model is: [18 072 Mä...
Consider an undamped system where the vector-matrix form of the system model is: [18 072 Mä +Kx = 08 |, [18000 - 7200 x -7200 8000 1-10 The system is initially at rest in equilibrium when it is put into motion with an initial velocity (0) = 120 while x,0) = x, 0) = 0 and «,(0) = 0. Use modal decomposition to find the system's free response.
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...
For the system below (a) Write equation of motions in matrix form (b) compute for the...
For the system below (a) Write equation of motions in matrix form (b) compute for the eigenvalues natural frequencies square) and (c) compute eigenvectors (mode shapes) vectors as j-1 (d) Sketch mode shapes r k3 k, k2 C2 m2 F. 2 Assume
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...
EXERCISE 2 The following system is composed by two bodies of mass m, and m2 and five identical strings of stiffness k....
EXERCISE 2 The following system is composed by two bodies of mass m, and m2 and five identical strings of stiffness k. Friction and any other dissipative terms are negligible. k Draw the free body diagrams for the two bodies. a) | y1 |F b) Write the equation of motion in matrix form, expressing the content of each matrix/vector m1 c) Calculate the natural frequencies of the system, knowing that m1 1 kg, m2 2 kg and k = 1000...
Consider an undamped system where the vector-matrix form of the system model is: F(t) [8 olx Mx + Kx = 0 18X, + 2000 -1800 x -1800 4500 I:1-[0] The system is initially at rest with x(0) = 0 and x,0)=0 when input F(t) = 84 sin15t is applied to the system. Use the modal decomposition method described in chapter 5 to find the system response. Some intermediate results (find these as part of your solution) are: The system's two...
Consider an undamped system where the vector-matrix form of the system model is: [F(t) [8 orë Mx + x = LO 183, 2000 -1800 x (-1800 45001 The system is initially at rest with X (0) = 0 and 2,0)=0 when input F(t) = 84 sin 15t is applied to the system. Use the modal decomposition method described in chapter 5 to find the system response. Some intermediate results (find these as part of your solution) are: The system's two...
The vector-matrix form of the system model is: (18 0 18000 72001 x f(t) or Mx + Kx = f(t) 08.3. -7200 8000 | X, 3. (1) X= M = (18 0 08 K 18000 -7200 7200 8000 and f(t) = (1) 12(0)] [x₂(t) The system's eigenvalues, natural frequencies, and eigenvectors are: 1 2 = 400, 0, = 20 s', and v, 1.5 1.) = 1600, 0), = 40 s', and v, = -1.5 1 1 The inverse of modal...
Consider an undamped system where the vector-matrix form of the system model is: [F(t) [18 07ž Mx + Kx = 083, + [18000 -72007x -7200 8000X, E]-[] The input to the system is F(t) = 6300 sin (30t). Use modal decomposition to find the system's frequency response. Note that the frequency response is the particular solution, and also called the steady-state response.
The vector-matrix form of the system model is: (18 0 18000 72001 x f(t) or Mx + Kx = f(t) 08.3. -7200 8000 | X, 3. (1) X= M = (18 0 08 K 18000 -7200 7200 8000 and f(t) = (1) 12(0)] [x₂(t) The system's eigenvalues, natural frequencies, and eigenvectors are: 1 2 = 400, 0, = 20 s', and v, 1.5 1.) = 1600, 0), = 40 s', and v, = -1.5 1 1 The inverse of modal...
Consider an undamped system where the vector-matrix form of the system model is: [18 072 Mä +Kx = 08 |, [18000 - 7200 x -7200 8000 1-10 The system is initially at rest in equilibrium when it is put into motion with an initial velocity (0) = 120 while x,0) = x, 0) = 0 and «,(0) = 0. Use modal decomposition to find the system's free response.
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...
For the system below (a) Write equation of motions in matrix form (b) compute for the eigenvalues natural frequencies square) and (c) compute eigenvectors (mode shapes) vectors as j-1 (d) Sketch mode shapes r k3 k, k2 C2 m2 F. 2 Assume
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...
EXERCISE 2 The following system is composed by two bodies of mass m, and m2 and five identical strings of stiffness k. Friction and any other dissipative terms are negligible. k Draw the free body diagrams for the two bodies. a) | y1 |F b) Write the equation of motion in matrix form, expressing the content of each matrix/vector m1 c) Calculate the natural frequencies of the system, knowing that m1 1 kg, m2 2 kg and k = 1000...
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