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problem 3 tk PROBLEM 3 Show that all solutions of the system: b X for any...
Problem 1: For the feedback system shown below, compute the transfer functions e/d, x/r. What are...
QUES 2!!!
Problem 1: For the feedback system shown below, compute the transfer functions e/d, x/r. What are the steady-state values for a constant d,r and when do they approach 0 asymptotically as t goes to infinity? C(s) 一心 - P(s) We were unable to transcribe this image
Problem 1: For the feedback system shown below, compute the transfer functions e/d, x/r. What are the steady-state values for a constant d,r and when do they approach 0 asymptotically as t...
12 Our treatment of the three-spring problem was incomplete because we looked only at the cosine parts of the solutions, ignoring the sines. (a) Show that the following equations are valid solut...
12 Our treatment of the three-spring problem was incomplete because we looked only at the cosine parts of the solutions, ignoring the sines. (a) Show that the following equations are valid solutions to Equations 6.1.1 and 6.1.2 for any constants A and A2 x (t) = Al cos (V/2 t) + A2 sin (v 2 ) (b) Show that the initial conditions h(0) = (0) = 0 lead to A2-0 and therefore to the solution we used in the Explanation...
Determine the values of a, if any, for which all solutions of the differential equation y''...
Determine the values of a, if any, for which all solutions of the differential equation y'' – (2a – 9)y' + (a? – 9a + 14)y = 0 tend to zero as t → 00; also determine the values of a, if any, for which all (nonzero) solutions become unbounded as t → . Solutions tend to zero as t + op as long as a (Click for List) A QE Solutions become unbounded as t → as long as...
Please answer a. - e. You are given a homogeneous system of first-order linear differential equations...
Please answer a. - e.
You are given a homogeneous system of first-order linear differential equations and two vector- valued functions, x(1) and x(2). <=(3 – )x;x") = (*), * x(2) (*)+-0) a. Show that the given functions are solutions of the given system of differential equations. b. Show that x = C1X(1) + czx(2) is also a solution of the given system for any values of cı and c2. c. Show that the given functions form a fundamental set...
Problem 11: a. Use the Laplace approach in order to obtain the analytical solutions x(t) for...
Problem 11: a. Use the Laplace approach in order to obtain the analytical solutions x(t) for the following Differential Equations using MATLAB (don't use DSOLVE): , Diff. Eqn. 1: * + 2x + 10x - Diff. Eqn. 2: 2x + 7* + 3x -0, *(0) - 0, X(0) - 3, *(0) - 0 4(0)-0
Exercise 1 Consider the system of differential equations 2 x= ( _ _3.)* (1) and let...
Exercise 1 Consider the system of differential equations 2 x= ( _ _3.)* (1) and let x("(t) = ( - ) 2 and x2(t) = ( _)er. a) Show that x(1) and x(2) are solutions of (1). b) Show that x = cıx(1) + c2x(2) is also a solution of (1) for any constants ci and c2. c) Show that x(1) and x(2) form a fundamental set of solutions. d) Find the solution of (1) that satisfies the initial condition...
i) Find all values of a for which all solutions of the differential equation y/ar 2)y = 0, x0 approach zero as x -+ 0....
i) Find all values of a for which all solutions of the differential equation y/ar 2)y = 0, x0 approach zero as x -+ 0.
i) Find all values of a for which all solutions of the differential equation y/ar 2)y = 0, x0 approach zero as x -+ 0.
Consider a (continuous-time) linear system x=Ax + Bu. We introduce a time discretization tk-kAT, ...
Consider a (continuous-time) linear system x=Ax + Bu. We introduce a time discretization tk-kAT, where ΔT = assume that the input u(t) is piecewise constant on the equidistant intervals tk, tk+1), , and N > 0, and N 1 a(t) = uk for t E [tk, tk+1). (a) Verify that the specific choice of input signals leads to a discretization of the continuous-time system x = Ax + Bu in terms of a discrete-time system with states x,-2(tr) and inputs...
6. The vectors x-[)and X - [-] are solutions vectors corresponding to the system of differential...
6. The vectors x-[)and X - [-] are solutions vectors corresponding to the system of differential equation X = AX (a) Use the Wronskian to show that X, and X, are linearly independent. (b) Write down a general solution to the system of equations. (e) Find the solution to the system subject to the initial condition X(0) -
Problem 5. (20 pts) Let ER be a positive real number and consider the damped system...
Problem 5. (20 pts) Let ER be a positive real number and consider the damped system modeled by the following second-order differential equation: y"(t) + yy' (t) + 25y(t) = 0, (a) Show that the long-term behaviour of all solutions is independent of y. (b) For which values of ye R+ does the above differential equation have oscillating solutions ? (i.e. solutions with infinitely many zeroes.) (c) Classify the above damped system into underdamped, critically damped and overdamped in terms...
QUES 2!!!
Problem 1: For the feedback system shown below, compute the transfer functions e/d, x/r. What are the steady-state values for a constant d,r and when do they approach 0 asymptotically as t goes to infinity? C(s) 一心 - P(s) We were unable to transcribe this image
Problem 1: For the feedback system shown below, compute the transfer functions e/d, x/r. What are the steady-state values for a constant d,r and when do they approach 0 asymptotically as t...
12 Our treatment of the three-spring problem was incomplete because we looked only at the cosine parts of the solutions, ignoring the sines. (a) Show that the following equations are valid solutions to Equations 6.1.1 and 6.1.2 for any constants A and A2 x (t) = Al cos (V/2 t) + A2 sin (v 2 ) (b) Show that the initial conditions h(0) = (0) = 0 lead to A2-0 and therefore to the solution we used in the Explanation...
Determine the values of a, if any, for which all solutions of the differential equation y'' – (2a – 9)y' + (a? – 9a + 14)y = 0 tend to zero as t → 00; also determine the values of a, if any, for which all (nonzero) solutions become unbounded as t → . Solutions tend to zero as t + op as long as a (Click for List) A QE Solutions become unbounded as t → as long as...
Please answer a. - e.
You are given a homogeneous system of first-order linear differential equations and two vector- valued functions, x(1) and x(2). <=(3 – )x;x") = (*), * x(2) (*)+-0) a. Show that the given functions are solutions of the given system of differential equations. b. Show that x = C1X(1) + czx(2) is also a solution of the given system for any values of cı and c2. c. Show that the given functions form a fundamental set...
Problem 11: a. Use the Laplace approach in order to obtain the analytical solutions x(t) for the following Differential Equations using MATLAB (don't use DSOLVE): , Diff. Eqn. 1: * + 2x + 10x - Diff. Eqn. 2: 2x + 7* + 3x -0, *(0) - 0, X(0) - 3, *(0) - 0 4(0)-0
Exercise 1 Consider the system of differential equations 2 x= ( _ _3.)* (1) and let x("(t) = ( - ) 2 and x2(t) = ( _)er. a) Show that x(1) and x(2) are solutions of (1). b) Show that x = cıx(1) + c2x(2) is also a solution of (1) for any constants ci and c2. c) Show that x(1) and x(2) form a fundamental set of solutions. d) Find the solution of (1) that satisfies the initial condition...
i) Find all values of a for which all solutions of the differential equation y/ar 2)y = 0, x0 approach zero as x -+ 0.
i) Find all values of a for which all solutions of the differential equation y/ar 2)y = 0, x0 approach zero as x -+ 0.
Consider a (continuous-time) linear system x=Ax + Bu. We introduce a time discretization tk-kAT, where ΔT = assume that the input u(t) is piecewise constant on the equidistant intervals tk, tk+1), , and N > 0, and N 1 a(t) = uk for t E [tk, tk+1). (a) Verify that the specific choice of input signals leads to a discretization of the continuous-time system x = Ax + Bu in terms of a discrete-time system with states x,-2(tr) and inputs...
6. The vectors x-[)and X - [-] are solutions vectors corresponding to the system of differential equation X = AX (a) Use the Wronskian to show that X, and X, are linearly independent. (b) Write down a general solution to the system of equations. (e) Find the solution to the system subject to the initial condition X(0) -
Problem 5. (20 pts) Let ER be a positive real number and consider the damped system modeled by the following second-order differential equation: y"(t) + yy' (t) + 25y(t) = 0, (a) Show that the long-term behaviour of all solutions is independent of y. (b) For which values of ye R+ does the above differential equation have oscillating solutions ? (i.e. solutions with infinitely many zeroes.) (c) Classify the above damped system into underdamped, critically damped and overdamped in terms...
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