Problem l: Determine whether the following models are stable, unstable, or neutrally stable: b, c. x-3x+10x...
4) Using the Routh-Hurwitz Criterion, determine whether the following Polynomials are Stable or Unstable. Please Show Supporting Work: 1) H(s) = s? + 10s + 5 = 0 Stable Unstable 11) H(s) = s4 +53 + 5s2 + 20s + 10 = 0 Stable Unstable 111) H(s) = 83 + 4Ks2 + (5 + K)s + 10 = 0 The Range of K for a Stable System is: a. b. K > 0.46 K< 0.46 0<K <0.46 Unstable for all...
For each of the following systems, find a > 0 and b > 0 such that L(x, y) = ax^2 + by^2 obeys d/dt(L) not = 0 whenever (x, y) 6= (0, 0). (This makes L a Liapounov function.) State whether the origin is a stable or unstable equilibrium in each case. (a) x' = −x^3 + 7xy^2 , y' = −3x^2y + y^3 . (b) x' = x^3 − y^3 , y' = 3xy^2 + 4x^2 y + 5y^3...
Problem : Consider the systems A and B whose roots are shown below BI 1. Regarding stability, the systems are a) b) c) d) Both stable Both unstable A is unstable and B is stable A is stable and B is unstable 2. The responses of the systems to step input are characterized as follows: a) Both are underdamped b) Both are overdamped c) A is underdamped and B is overdamped d) A is overdamped and B is underdamped 3....
Subtract (3x-30) from the sun of (-2x+8) and (9x-12). A. 8x +50 B. 10x-34 C. 4x+26 D. -4x-26
Write the quadratic function in the form f(x)=a(x-h)^2+k; Find the vertex and graph the function (a) f(x)=x^2-6x (b) f(x)=-x^2+4x+1 (c) f(x)=3x^2-10x+2
Problem l: (13 pts) mper system subject to a constant force is described by the following equation of motion and associated initial displacement and velocity, + 10x + 25x 150 with x(0) 5 and x(0) 2 (1) Solve for x(t) (5 pts). (2) What is the steady state solution? (2 pt) (3) What is the transient solution? (1 pt) V(4) Is the system stable or unstable? (1 pt) (5) What is the free solution (2 pts) (6) What is the...
III) Consider the following differential equation: 5•(t) + 3x(t) - 4 = 0, x(0) = 2. 1. Find the backward solution. 2. Is this solution convergent or divergent? Justify your answer. 3. Determine the stationary solution and indicate whether it is stable or unstable. 4. Sketch a phase diagram and a time-path diagram.
Each of the following equations specifies an LTID system. Determine whether these systems are asymptotically stable, unstable, or marginally stable. 9.6-1 (a) yk 20.6y[k + 1] - 0.16y[k] = f k + 1 - 2flk] (b) (Е? (c) (E 1Ey{k] = (E + 2)fjk] (d) yk2y(k]0.96y(k - 2] 2flk - 1] +3f(k - 3] (e) (E2- 1)(E +E+1)уk] 3DEflk] +1)yk fk] Each of the following equations specifies an LTID system. Determine whether these systems are asymptotically stable, unstable, or marginally...
l. Determine the real root(s) off(x)--5xs + 14x3 + 20x2 + 10x a. Graphically on a graph paper. b. Using Bisection method c. Using False Position method to determine the root, employing initial guesses of x-2 d. Using the Newton Raphson methods to determine the root, employing initial guess to determine the root, employing initial guesses ofxn-2 and Xu-4 and Es= 18%. and r 5.0 andas answer. 1%. was this method the best for these initial guesses? Explain your xo--l...
Determine whether the following transformations are linear. A) T(x, y) = (3x, y, y ? x) of R2 ? R3 B) T(x, y) = (x + y, 2y + 5) of R2 ? R2