Now consider that the system described in Problem 1 is opeted at steady state Your task is to fin...
We know that a country reaches a steady state when investment equals depreciation. This means Consider an economy with the production function Squaring both sides and solving for K yields y2 Substituting K into the steady state equation gives Y2 A2 Solve this equation for Y. Divide both sides by Y and put everything on the other side to solve for Y. Once you do this, use this cquation to answer the question about the cconomy in the steady state...
3. Steady-State CSTR Assume you have an adiabatic CSTR operating at steady-state. Within the CSTR, reactant A is being converted to product, where the rate of reaction is first order: A =kC However, the reaction is also exothermie, and the rate constant is described through the classic Arrhenius equation: k(T) = k e RT Under the set of conditions given, solve for the temperature (T) and the concentration (CA) leaving this CSTR operating under steady-state conditions. k . CA0| 3000...
Need help doing problem 1 and 2
Problem #1: Determine the steady state solution for the given initial conditions: f"(t)+2f'(t) +5f(t)=0.5; for f'(0)=f(t)=0 Problem #2: use both the partial fraction approach and rows #22 and 23 from the Laplace table. F(s)=(3+3)/(s^2+35+2)
Just 5-8
1 Analytics of the Solow Model In the Solow economy, people consume a good that firms produce with technology Y (which we assume to be constant) and f is a Cobb-Douglas production function Af (K, L), where A is TFP f(K, L) KL-a Here K is the stock of capital, which depreciates at rate δ E (0, 1) per period, and L is the labor force, which grows exogenously at rate n > 0. Here employment is always...
1. Consider the problem of steady state heat flow in the half-plane, 22T a2T + ar2 =0 for ER and y>0, ay2 subject to the boundary condition T(3,0) = g(x), and T +0 as yo. You will solve the problem using the Fourier transform in 2, with T(w,y) = ZELT(, y)e-iw= ds 2 (a) Derive an ODE for T. You can assume T +0 as|a . (b) Derive conditions for I at y = 0 and as y. You can...
Question 1 Determine the steady-state response (t) for the network in the figure below 8 F 2 H 1? 7cos 2t V i1(tl) io(t) If the steady-state response is given by io (t) = 1° cos (21+ ?), find the values of 1, and q. Express qin the range [-180°, 180°). Click if you would like to Show Work for this question: Open Show Work
Problem 2(30 points) Consider the steady-state temperature distribution in a square plate with dimensions 2 m x 2 m. There is a heat generation of ġ(x.y)=6x [W/my], and the thermal conductivity of k=1[W/(m-°C)]. The temperature on the top boundary is given by a piecewise function, f(x), which is defined below. x(4- x²)+10 0<x<1 | x(4- x?) + 20, 1<x<2 The bottom boundary is insulated. The temperatures on left-handed and right-handed boundary are maintained at constants 10[°C] and 20 [°C] as...
1 Steady State and Covid-19 Shock In this section, suppose that productivity does not vary over time but is con- stant: A+ = A > O for all t. 1. Find the expression known as the law of motion of the equilibrium stock of capital. To this end, write down the market clearing condition of the capital market for period t +1 and substitute the expression that you found before for St+1. Use other equilibrium conditions (the equilibrium expression for...
8. Consider the LTI system described by the differential equation in Problem 2.5-1. Solve the (forced) response of the system to the following everlasting signals: (a) ft) 1, (b) ftet, (c) f(t) = 100cos(2t- 60°) Using the classical method, solve 2.5-1 (D +7D+12) ye) (D+ 2)f(¢} (0*)= 0, s(0+ ) = 1, and if the input f(t) is if the initial conditions are
8. Consider the LTI system described by the differential equation in Problem 2.5-1. Solve the (forced) response...
Question 1 [Total 20 marks] (a) [5 marks] In a steady-state two-dimensional heat flow problem, the temperature, u, at any point in the domain (t, ) satisfies the differential equation u y(2-y) u= U0F With the given temperature boundary condition as follows: u(x, 0) = 0, u(x, 2) = x(4-x), 0 < x < 4 Calculate the temperature at the interior points a, b, and c using a mesh size h-1.
Question 1 [Total 20 marks] (a) [5 marks] In...