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Using the Routh table, tell how many poles of the following function are in the right half-plane. in the left hall-plane, and on the
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Control Systems Engineering
- The one-dimensional harmonic oscillator has the Lagrangian L = mx˙2 − kx2/2. Suppose you did not know the solution of the motion, but realized that the motion must be periodic and therefore could be described by a Fourier series of the form x(t) =∑j=0 aj cos jωt, (taking t = 0 at a turning point) where ω is the (unknown) angular frequency of the motion. This representation for x(t) defines many_parameter path for the system point in configuration space. Consider the action integral I for two points t1 and t2 separated by the period T = 2π/ω. Show that with this form for the system path, I is an extremum for nonvanishing x only if aj = 0, for j ≠ 1, and only if ω2 = k/m.arrow_forwardnk int m The spring-mass-system shown in the figure has the following parameters: spring constant k = 4 N/m; mass m 6 %3D kg and the constant n = 1.6. M is the corresponding mass-matrix of the system. V1 and V2 are the eigenvectors associated with the smallest and largest natural frequencies of the system, respectively. If V,TV, = 1 and V2 V2 = 1, then what is value of V,™MV2 (in kg)? Answer:arrow_forwardA door stopper spring is held at an angle from its equilibrium position and then released, and the angular velocity of the plastic end is given by the function: w(t) = 3e-0.2t cos(7t) 1. Find its angular acceleration function a (t). 2. Find its angular displacement function 0 (t), assuming 0 (0) 0. 3. If the rotational motion is confined to the xy plane, what is the direction of the acceleration at t-0? Justify your answers with your rationale and equations used.arrow_forward
- 7- In the two phase method if Max z* < 0 and at least one artificial vector appear in the optimum basic at a positive level (Aj 2 0). we proceed to phase -2.* true Falsearrow_forwardConsider the following rotational mechanical system, a. Apply the "by inspection" method in Laplace domain to write the system of equations that represents the dynamics of the system b. Solve for the output variable q1(s). Use Cramer's rule or the substitution method to solve for the output variable q1(s). c. Give the transfer function G(s) = 91(s)/T(s) 0₁ (1) T(1) J1 82(1) oför J2 oooo K₁ K2 oooo Darrow_forward4.78. Demonstrate that the system modes are orthogonal with respect to the [M] and [K] matrices for the following system: 10 0 0 (, 8-8 500 -50 X1 2 0 *2 + -50 400 -20 0 4 0 - 20 100 X3arrow_forward
- Obtain the Fourier series expansion for the following function 0arrow_forwardPleasearrow_forwardCopy of Based on the kinematic system below If we rotate (A-B) 90 degrees counter-clockwise, and (B-P) 90 degrees clockwise where will be the point P y (2,4) Kinematic skeleton 42) O (4,4) (4,6) (6,4) O (6,6)arrow_forwardQ5. For a point at distance 50 m and angle 450 to the axis which of the following statements are correct? Consider an infinite baffled piston of radius 5 cm driven at 2 kHz in air with velocity 10 m/s. You may choose multiple options. a. The constant term is given by 515.03 b. The distance dependent term is given by e-jk50/50 c. The directivity term is given by j1(Ka sin 450)/sin 450 d. There is no time dependent term.arrow_forwardKnowing that u c(t) it is the unit step function, the inverse Laplace Transform of the function F(s)= e-s(s-2)/s2 - 4s +3 is: a) f(t) = u1(t) e2(t-1) cosh(t - 1) b) f(t) = u1(t) e2(t-1) cosh(t) c) None of the answers d) f(t) = u2(t) e2(t-1) cosh(t - 1) e) f(t) = u2(t) e2(t-1) cosh(t - 2)arrow_forwardLet C be the line segment joining A(-1,1, -2) to 0(0,0,0). A parameterization of C is given by * O x=-t,y=t,z=-2t, Osts1 O x=-t+1,y=t+1,z=-2t-2, Osts1 O x=-t-1,y=t+1,z=-2t-2, Osts1 x=t-1,y=-t+1,z=2t-2, Osts1 None of thesearrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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