A system is described by the following differential equation:
Find the expression for the transfer function of the system, Y(s)/X(s). [Section: 2.31]
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Control Systems Engineering
- Solve the system of linear equations. x+y+z = -6 x-6y-7z = -29 -7y-5z = 4 O (-8, -7,9) O (-6, -7, 10) O (-7,-8, 9) O (-7,-6, 10) O (9,-7,-8)arrow_forward- The projection of the vector i+3j+7k on the vector 2î + 6j+3k is: a: 41 41 b: 7V59 41 c: V59 d: 4arrow_forward-Find Taylor or Maclaurin for the following functions: 4) f(x) = x3 – 2x + 4 at a = 1arrow_forward
- = Find the general solution to the following 2nd Order O.D.E., where y" y" + y + y = 0 (³x) - ₂ - C₂ sin sin (√³7)} ○ y(x) = e. {c₁ cos (³0) - -x)+ + C₂ sin(x)} y(x) = e{c₁ cos y(x) = e{c₁ cos(x) + ₂ sin(x)} ○ y (x) = c₁ · e¯7 · cos (³x) + c₂ · ež · sin (√³x) ○ y(x) = c₁ ·e· cos(x) + c₂ · €¯ · sin (³x) d² y(x) dx²arrow_forwardLet f be any non-zero real valued function in x and y and R be a closed bounded region above the x-axis. Then the double integral of f over R is always positive * False Truearrow_forwardIf f(x.y,z) = xy+ yz + xz. The maximum rate of change of f at the point P(1,2,3) is: %3D 50 O 11 O 5V2 32arrow_forward
- Find a vector x whose image under T, defined by T(x) = Ax, is b, and determine whether x is unique. Let 1 3 6 15 4 15 27 69 0 1 1 -4 - 13 - 25 A= b= x= 3 - 63 Find a single vector x whose image under T is b. s the vector x found in the previous step unique? O A. Yes, because there are no free variables in the system of equations. O B. Yes, because there is a free variable in the system of equations. O C. No, because there are no free variables in the system of equations. O D. No, because there is a free variable in the system of equations.arrow_forwardShow me step by steparrow_forwardQ1 A three-level offshore platform located in the Helang Oilfield area has a 1500 kg floor steel grating supported at each level. The structure sometimes is subjected to a vertical ocillation movement during rough sea waves given by function of y(t) = Y sin ot If the steel grating only moves in the vertical direction and is supported by one equivalent spring and damper at each steel grating pole level with stiffness, k, = (300 xT) Nim, k= (200 x T) Nm and k = (100 × T) Ním while damping, c: = (15 x U) Nsm, c: = (10 x U) Ns'm and c; = (5 x U) Nsim, respectively, as simplified in Figure Q1. Neglect the effect of gravitational force. Use T=4 and U = 6 Table 1 5th digit of matric number 6th digit of matrix number T 4 1 4 1 4 2 3 3 6 4 4 6. 5 3 6. 6. 2 6 7 2 7 1 6. 1 (a) Sketch a free body diagram for each steel grating that includes the mass's action and reaction forces. (b) Determine the equation of motion in a matrix form using Newton's second law, [m]ÿ + [clý + [k]y = F. (c) By omitting…arrow_forward
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