Draw by hand the Bode plot of the following systems 1. 50 G(s) s(s² + 4s + 8)
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- Derive the governing differential equation for each system with the chosen generalized coordinate. SEE THE IMAGE BELOW Answers: 1. GDE: (5/2) mẍ + (5/4) kx = 0 2. GDE: (7/48) mL² ϴ [note: theta symbol has two dots above) + (3/8) cL² ϴ [ note: theta symbol has one dot above] + 5 kL² ϴ = 0A velocity of a vehicle is required to be controlled and maintained constant even if there are disturbances because of wind, or road surface variations. The forces that are applied on the vehicle are the engine force (u), damping/resistive force (b*v) that opposing the motion, and inertial force (m*a). A simplified model is shown in the free body diagram below. From the free body diagram, the ordinary differential equation of the vehicle is: m * dv(t)/ dt + bv(t) = u (t) Where: v (m/s) is the velocity of the vehicle, b [Ns/m] is the damping coefficient, m [kg] is the vehicle mass, u [N] is the engine force. Question: Assume that the vehicle initially starts from zero velocity and zero acceleration. Then, (Note that the velocity (v) is the output and the force (w) is the input to the system): 1. What is the order of this system?A velocity of a vehicle is required to be controlled and maintained constant even if there are disturbances because of wind, or road surface variations. The forces that are applied on the vehicle are the engine force (u), damping/resistive force (b*v) that opposing the motion, and inertial force (m*a). A simplified model is shown in the free body diagram below. From the free body diagram, the ordinary differential equation of the vehicle is: m * dv(t)/ dt + bv(t) = u (t) Where: v (m/s) is the velocity of the vehicle, b [Ns/m] is the damping coefficient, m [kg] is the vehicle mass, u [N] is the engine force. Question: Assume that the vehicle initially starts from zero velocity and zero acceleration. Then, (Note that the velocity (v) is the output and the force (w) is the input to the system): A. Use Laplace transform of the differential equation to determine the transfer function of the system.
- sole using laplace transforms Do not answer in image formatIn this exercise we show that in the general case, exact recovery of a linear compression scheme is impossible. a. Let A ∈ Rn,d be anarbitrary compression matrix where n ≤ d−1. Show that there exists u,v ∈ Rd,u= v, such that Au = Av. Hint: Show that there exists u= 0,v = 0 such that Au = Av = 0. Hint: Consider using the rank-nullity theorem. b. Conclude that exact recovery of a linear compression scheme is impossible.Consider the thermocouple properties you found in the question "Temperature of a thermocouple (1/3)" If the thermocouple is initially outside of the bath at room temperature (20 °C), what is the maximum temperature it will register if it's instantaneously inserted into the batch (55 °C) for 18 seconds and then removed? Use an inverse Laplace transform to find the solution. a. 32.68 °C b. 44.97 °C c. 64.97 °C d. 12.68 °C
- OBLEM 4. Using the condition (3.027) of Lect. 16, prove that the mo- mentum operator p is Hermitian. HINT: Use the periodic boundary conditions for the functions g(r) and s(x).Heat, q is a path function. a) True b) FalseThe steady-state response is the part of the Total Response which does not approach infinity as time approaches infinity. True False