Can you help me by providing the MATLAB code? We will consider a linear system and a nonlinear system under uncertainty, each expressed in the formof a set of stochastic differential equation (SDE) as follows:da (Ar+ Bu)dt+ Gdw,da f(x,u,t)dt+Gdw,(1)ཌས(2)where x is the state, u is the control, and dw is a differential increment of standard Brownian motion, i.e.,E[dw] = 0 and E[dw(t)dw(t)] = dt-1.Problem Set 9 Linear Stochastic ProcessIn this problem, we consider the linear SDE, Eq. (1), with a very simple model where 2 € R², u = [0,0](no control), and dw R². The matrices A, B, and G are given as follows:A=02x2, B=02x2, G= [002(3)where σp E R represents the degree of the uncertainty, and let us take ₁ = 2 and 2-3. Assume that theinitial state is deterministic and (t = 0) = [0,0]. Take the following steps to simulate the given SDE fort€ [0, 1]:Perform Monte Carlo simulation (again M = 20) by propagating the linear SDE with the approx-imated Brownian motion, and show the time history of each element of over time; include 3-0bounds (i.e., ±30) in the plot and discuss the consistency.

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Answered: We will consider a linear system and a…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

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We will consider a linear system and a nonlinear system under uncertainty, each expressed in the form of a set of stochastic differential equation (SDE) as follows: = da (Ax+ Bu)dt + Gdw, dx = f(x,u,t)dt+Gdw, (1) (2) where x is the state, u is the control, and dw is a differential increment of standard Brownian motion, i.e., E[dw] = 0 and E [dw(t)dw(t)] = dt-1. In this problem, we consider the linear SDE, Eq. (1), with a very simple model where x = R², u = [0,0] (no control), and dw R². The matrices A, B, and G are given as follows: A=02x2, B=02x2; G = [000] (3) where σp Є R represents the degree of the uncertainty, and let us take σ₁ = 2 and σ2 = 3. Assume that the initial state is deterministic and e(t = 0) = [0,0]. Take the following steps to simulate the given SDE for 1 € [0, 1]: (a): Consider the increments of w between each time interval [+1). Derive the analytical expression of Aw using w~N(02, 12), where Aw, w(tk+1) — w(tk). (c): Derive the approximate continuous-time EoM from…
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Can you use MATLAB to help me solve part (d)
The stress profile shown below is applied to six different biological materials: Log Time (s] The mechanical behavior of each of the materials can be modeled as a Voigt body. In response to o,= 20 Pa applied to each of the six materials, the following responses are obtained: 2 of Maferial 6 Material 5 0.12 0.10 Material 4 0.08 Material 3 0.06 0.04 Material 2 0.02 Material 1 (a) Which of the materials has the highest Young's Modulus (E)? Why? Log Time (s) (b) Using strain value of 0.06, estimate the coefficient of viscosity (n) for Material 6. Stress (kPa) Strain
The relative displacement u(t) of a single-storey shear building subjected to an earthquake ground motion is represented by the following second-order linear ordinary differential equation: d?u dt2 du + c + ku = a, (t) m dt where m, c, and k are the mass (kg), damping constant (Ns/m), and stiffness of the structure (N/m), respectively. Meanwhile, a,(t) is the function of earthquake ground acceleration. Suppose the building with a mass of 2000 kg and supported by columns of combined stiffness of 32 x 103 N/m is subjected to earthquake with ground acceleration given by the following function: ag(t) = 36000 cos 2t Find the equation of the displacement, u(t), given the damping is not installed to the building. Then, find how much the building is displaced from t =30 seconds to t =60 seconds of earthquake.
Can you help me by providing the solutions in MATLAB code?
Manufacturing process with two variables x1,x2 described by the empirical model: y=bo +b1 x1 + b2 x2 + b12 x1 x2 + b3 (x1)^2 +b4 (x2)^2 please refere to the image attached
An object attached to a spring undergoes simple harmonic motion modeled by the differential equation d²x = 0 where x (t) is the displacement of the mass (relative to equilibrium) at time t, m is the mass of the object, and k is the spring constant. A mass of 3 kilograms stretches the spring 0.2 meters. dt² Use this information to find the spring constant. (Use g = 9.8 meters/second²) m k = + kx The previous mass is detached from the spring and a mass of 17 kilograms is attached. This mass is displaced 0.45 meters below equilibrium and then launched with an initial velocity of 2 meters/second. Write the equation of motion in the form x(t) = c₁ cos(wt) + c₂ sin(wt). Do not leave unknown constants in your equation. x(t) = Rewrite the equation of motion in the form ä(t) = A sin(wt + ), where 0 ≤ ¢ < 2π. Do not leave unknown constants in your equation. x(t) =
The pressure rise, Ap across a centrifugal pump from a given manufacture can be expected to depend on the angular velocity of the impeller w, the Diameter D, of the impeller, the volume flow-rate Q, and the density of the fluid, p. By using the method of repeating variables show that Др ρω- D wD³ A model pump having an impeller diameter of 0.200 m is tested in the laboratory using water. The pressure rise when tested at an angular velocity of 407 rad/sec is shown on the graph. What would be the pressure rise for a geometrically similar pump with an impeller diameter of 0.30 m used to pump water operating at an angular velocity of 807 rad/sec and at a flow rate of 0.070 m³/s? Sol: 40 30 (kPa) Apm 10 0 € 0.02 Q Model data (₁ = 40 rad/s Dm = 20 cm 0.04 0.06 Qm (cubic meters per sec) 0.08
Q2 Consider a conical receiver shown in Figure 2. The inlet and outlet liquid volumetric flow rates are Fl and F2, respectiveily. ccorresponding radius in r) Figure 2 Conicul tank Develop the model equation with necessary assumption(s) with respect to the liquid height h. ii. What type of mathematical model is this? 1 R %3D Hint: Model: = F, – Fz, where the volume V=r h=nh, since = substitute V and Fz expressions and get the final form. %3D %3D %3D dt H.
3. Consider the mechanical system shown in Fig. 3. Let V3(t) be the input and the acceleration of the mass be the output. Derive the state equations and the output equation using linear graphs and normal trees. V,(t) В m k2 101 k, Figure 3: A mechanical system with an across-variable source
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