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
- Find the general solution for the following differential equation (r +3). fip + (x+ 4)y = x²e- = r*e drarrow_forwardThe differentials of point functions are exact differentials. Select one: O True Falsearrow_forwardSolve for x and y in terms of z of the given system below. 2х + 5y- 5х— Зу + -2z %3D4 6z = 5arrow_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_forwardA. Find the values of a such that vectors and are orthogonal. B. Find the domains of the vector-valued function 7(t) = e' i+ j+ In(t? – 4) karrow_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_forwardIn the Figure 2, the resultant R can be found as: R* Figure 2: R. R? = P² + Q? - 2PQ cos B O True O Falsearrow_forwardIn the Figure 2, the resultant R can be found as: R* Figure 2: R P. R? = P2 + Q? - 2PQ cos B O True O Falsearrow_forward
- 3. An oscillator is subject to an external driving force F(t), which is an exponentially decreasing function of time t: F(t) = {Foe-at Find the position of the oscillator at any time t. t20 t<0arrow_forwardfind a real general solution: * y + 4y' + 5y =x +2arrow_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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