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 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.
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.
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...
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-1440 2880 and f(t) = -[10] Find the following without using linear algebra software or calculator functions: a) The system's natural frequencies and mode shapes. b) The mass-normalized matrix V that makes VTMV=I.
2 Homogeneous coordinates Recall that an affine function is of the form f^x) Mx + t for a matrix M and vector t. Homogeneous coordinates are frequently used to represent affine functions in robotics and 3D graphics. We define the function H by and if f-x) Mxtt where then C0 a. Some vectors are valid homogeneous representations of vectors, and some are not. Explain how to tell if some vector y-0 is the homogeneous representation of some other vector -y...
For the following system: -13 1 0 x(t)30 01x(t)u(t) y(t)=[1 이 x(t) 0 a. Determine if the system is completely controllable. b. If the system is completely controllable, design a state feedback regulator of the form u(t)-Kx(t) to meet the following performance criteria: %10 1.5% · T, = 0.667 sec For the following system: -13 1 0 x(t)30 01x(t)u(t) y(t)=[1 이 x(t) 0 a. Determine if the system is completely controllable. b. If the system is completely controllable, design a...
Write the given system in the matrix form x' = Ax+f. r(t) = 7r(t) + tant e' (t) = r(t) - 90(t) – 5 Express the given system in matrix form.
(4) Consider the 2nd order equation for a mass-spring-damper system, mx'' + bx' + kx = f(t) a) Assuming f(t) is a step function, find the Laplacian transform, X(s) (include terms for the initial conditions xo, vo). b) Assume m = 1, b = 5, and k = 6, and x(0) = 3, x’(0) = 0. Find the time-domain solution (take the inverse transform). (5)Find the Laplace transform of y(t) from the differential equation, assuming u(t) is a step function....