Problem 5 Consider the linear system [1 2 0 2 -4 7x(t) 1 -4 6 y(t) [1 -2 2] (t). (4) a(t = (a) Is the system (4) observable? (b) Give a basis for the unobservable subspace of the system (4). In the remainder of this problem, consider the linear system а — 3 8— 2а 0 1 2a u(t) (t) (5) x(t) = with a a real parameter. (c) Determine all values of a for which the system (5)...
Solve the initial value problem with 4 x'(t) = A, fort > O with x(0) = Classify the nature of the origin as an attractor, repeller, or saddle point of the dynamical system described Ax=b. Find the directions of greatest attraction and/or repulsion. x(o)= [1] A-[18 -16] -2 - 4 10 -16 2 -120 1 a. x(t)= (0,0) is a saddle point 5 2 120 b. x(t)= 1 + 6 le -61 (0,0) is an attractor 5 C. x(t)= o[1]...
Solve the following system of DEs with initial conditions x (0) = 2, and (0) = 4, x 0 (0) = 0, and Y 0 (0) = 0 In this problem x = x (t) and y = y (t). Indicate in order the values of A, B, C, and D (B <D) so that x (t) = Ae^(Bt) + C e^(Dt) be the solution x (t). Answer:8. Resuelva el siguiente sistema de EDs con condiciones iniciales x(0) 2, y(0...
Would like the full steps to get to the answer. Thank you. 6. Find a solution u(x, t) of the following problem 9u 4 0 Utt u(0, t) u(4, t) 0 0 x2 2 4 ut(r, 0) 0 u(r, 0) 4 6. Find a solution u(x, t) of the following problem 9u 4 0 Utt u(0, t) u(4, t) 0 0 x2 2 4 ut(r, 0) 0 u(r, 0) 4
Problem 4. Convolve the following input X(t) with the system impulse response h(t) and plot the system output y(t). h(t) Problem 5. Construct a Bode plot of the input impedance DMM 100nF zin - 300F CM 500 ohms
Problem 1: Let the impulse response of an LTI system be given by 0 t< h(t) = 〉 1 0 < t < 1 0 t>1 Find the output y(t) of this system if the input is given by a) x(t) = 1 + cos(2nt) b) x(t)-cos(Tt) c) x(t) sin (t )l d) x(t) = 1 0 < t < 10 0 t 10 e) x(t) = δ(t-2)-5(t-4) f) a(t)-etu(t) Problem 2: For the same LTI system in Problem 1,...
6. Solve the following boundary value problem: 1 U = 34xx, 0 < x < 1,t> 0; u(0,t) = u(1,t) = 0; u(x,0) = 7 sin nx - sin 31x
For the following system: -13 1 0 x(t)30 01x(t)u(t) y(t)=[1 이 x(t) 0 a. Determine if the system is completely controllable. b. If the system is completely controllable, design a state feedback regulator of the form u(t)-Kx(t) to meet the following performance criteria: %10 1.5% · T, = 0.667 sec For the following system: -13 1 0 x(t)30 01x(t)u(t) y(t)=[1 이 x(t) 0 a. Determine if the system is completely controllable. b. If the system is completely controllable, design a...
Problem #6: Find the Laplace transform of the following functions 4 0<t 3 9 tz3 (a) f(t) (b) f(t) 9>10 7 0 t2 6 0 t</9 cos[10(/9) tz n/9 f(f = symbolic Enter your answer as a function of s, as in these examples Problem #6(a): symbolic Enter your answer as a function of s, as in these examples Problem #6(b): Enter your answer as a symbolic function of s, as in these examples Problem #6(c): Problem #6: Find the...