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Chapter 7, Section 7.1, Question 07ab Transform the given system into a single equation of second-order....
Transform the given system into a single equation of second-order x'= -821 + 7:02 2 =...
Transform the given system into a single equation of second-order x'= -821 + 7:02 2 = -721 - 822- Then find 21 and 22 that also satisfy the initial conditions Then find 2, and are that alene 21 (0)=9 22 (0) = 2. Enter the exact answers. Enclose arguments of functions in parentheses. For example, sin (23).
Transform the system into a single equation of second-order x' = 31.21 - 3002 r'a =...
Transform the system into a single equation of second-order x' = 31.21 - 3002 r'a = 3001 - 3022 and find 21 and 22 that also satisfy the following initial conditions: x1(0) = 9 *20) = 3
Consider the following. Xi' = 3x1 - 2x2 x1(0) = 3 xz' = 2x1 – 2x2,...
Consider the following. Xi' = 3x1 - 2x2 x1(0) = 3 xz' = 2x1 – 2x2, *2(0) = (a) Transform the given system into a single equation of second order by solving the first equation for x2 and substitute into the second equation, thereby obtaining a second order equation for X1. (Use xp1 for xı' and xpP1 for x1".) xpP1 – xP1 – 2x1 = 0 (b) Find X1 and x2 that also satisfy the initial conditions. *2(t) =
7. Systems of first order equations higher order. Consider the system can sometimes be transformed into...
7. Systems of first order equations higher order. Consider the system can sometimes be transformed into a single equation of xf xx12x2 = -2x1 + X2, (a) Solve the first equation for x2 and substitute into the second equation, thereby obtain- ing a second order equation for x1. Solve this equation for x1 and then determine x2 also (b) Find the solution of the given system that also satisfies the initial conditions x\ (0) = 2, x2 (0)= 3
Second order systems of ordinary differential equations (ODE) often describe motional systems involving multiple masses. Solve the following second order system of ODE using Laplace transform meth...
Second order systems of ordinary differential equations (ODE) often describe motional systems involving multiple masses. Solve the following second order system of ODE using Laplace transform method: Xy-=5x1-2x2 + Mu(t-1) x2-=-2x1 + 2x2 x,(t) and x2(t) refer to the motions of the two masses. Consider these initial conditions: x1 (0) = 1, x; (0)-0, x2(0) = 3, x(0) 0
Second order systems of ordinary differential equations (ODE) often describe motional systems involving multiple masses. Solve the following second order system...
Chapter 7, Section 7.5, Question 20 Solve the given system of equations. Assume t 0 ty...
Chapter 7, Section 7.5, Question 20 Solve the given system of equations. Assume t 0 ty Hint: The system tx - Axis analogous to the second order fuer equation. Assuming that X-&', where is a constant vector, and I must satisfy (A-DE- On order to obtain rontva solutions of the given differential equation 0 T = + C2 0 -6 X = Cil +cal -4 X=Cl cal x = Ci 0 x=c;( +4}++ c3(-6)***
(b) [6 points) Transform the given initial value problem for the single differential equation of second...
(b) [6 points) Transform the given initial value problem for the single differential equation of second order into an initial value problem for two first order equations. (Do not attempt to solve it!) u" + -u' +4u= 2 cos(3t), u(0) = 1, u'(0) = -2.
Please assist with the following using Laplace Transform The second order differential equation of a vibratıng...
Please assist with the following using Laplace
Transform
The second order differential equation of a vibratıng system is given by d2 dt'dt 5 1 Determine the system transfer function with initial conditions y(0) y(0)0 5 2 Determine the response of the system, y(t), with a unit step input r(t) and intial conditions y(0)1 and y(0) -1 (15)
Chapter 3, Section 3.3, Question 02 Consider the given system of equation. 2 -4 X 6 -8 (a) Find the general solution of...
Chapter 3, Section 3.3, Question 02 Consider the given system of equation. 2 -4 X 6 -8 (a) Find the general solution of the given system of equation 1 +c2e2t VI The general solution is given by X (t) = ci where V2. |and 21 >A2 =| ; vi = and v2 (b) Draw a direction field and a phase portrait. Describe the behavior of the solutions as t - o. 1) If the initial condition is a multiple of...
Problem 3. Consider the initial value problem w y sin() 0 Convert the system into a single 3rd order equation and solve resulting initial value problem via Laplace transform method. Express your answ...
Problem 3. Consider the initial value problem w y sin() 0 Convert the system into a single 3rd order equation and solve resulting initial value problem via Laplace transform method. Express your answer in terms of w,y, z. Problem 4 Solve the above problem by applying Laplace transform to the whole system without transferring it to a single equation. Do you get the same answer as in problem1? (Hint: Denote W(s), Y (s), Z(s) to be Laplace transforms of w(t),...
Transform the given system into a single equation of second-order x'= -821 + 7:02 2 = -721 - 822- Then find 21 and 22 that also satisfy the initial conditions Then find 2, and are that alene 21 (0)=9 22 (0) = 2. Enter the exact answers. Enclose arguments of functions in parentheses. For example, sin (23).
Transform the system into a single equation of second-order x' = 31.21 - 3002 r'a = 3001 - 3022 and find 21 and 22 that also satisfy the following initial conditions: x1(0) = 9 *20) = 3
Consider the following. Xi' = 3x1 - 2x2 x1(0) = 3 xz' = 2x1 – 2x2, *2(0) = (a) Transform the given system into a single equation of second order by solving the first equation for x2 and substitute into the second equation, thereby obtaining a second order equation for X1. (Use xp1 for xı' and xpP1 for x1".) xpP1 – xP1 – 2x1 = 0 (b) Find X1 and x2 that also satisfy the initial conditions. *2(t) =
7. Systems of first order equations higher order. Consider the system can sometimes be transformed into a single equation of xf xx12x2 = -2x1 + X2, (a) Solve the first equation for x2 and substitute into the second equation, thereby obtain- ing a second order equation for x1. Solve this equation for x1 and then determine x2 also (b) Find the solution of the given system that also satisfies the initial conditions x\ (0) = 2, x2 (0)= 3
Second order systems of ordinary differential equations (ODE) often describe motional systems involving multiple masses. Solve the following second order system of ODE using Laplace transform method: Xy-=5x1-2x2 + Mu(t-1) x2-=-2x1 + 2x2 x,(t) and x2(t) refer to the motions of the two masses. Consider these initial conditions: x1 (0) = 1, x; (0)-0, x2(0) = 3, x(0) 0
Second order systems of ordinary differential equations (ODE) often describe motional systems involving multiple masses. Solve the following second order system...
Chapter 7, Section 7.5, Question 20 Solve the given system of equations. Assume t 0 ty Hint: The system tx - Axis analogous to the second order fuer equation. Assuming that X-&', where is a constant vector, and I must satisfy (A-DE- On order to obtain rontva solutions of the given differential equation 0 T = + C2 0 -6 X = Cil +cal -4 X=Cl cal x = Ci 0 x=c;( +4}++ c3(-6)***
(b) [6 points) Transform the given initial value problem for the single differential equation of second order into an initial value problem for two first order equations. (Do not attempt to solve it!) u" + -u' +4u= 2 cos(3t), u(0) = 1, u'(0) = -2.
Please assist with the following using Laplace
Transform
The second order differential equation of a vibratıng system is given by d2 dt'dt 5 1 Determine the system transfer function with initial conditions y(0) y(0)0 5 2 Determine the response of the system, y(t), with a unit step input r(t) and intial conditions y(0)1 and y(0) -1 (15)
Chapter 3, Section 3.3, Question 02 Consider the given system of equation. 2 -4 X 6 -8 (a) Find the general solution of the given system of equation 1 +c2e2t VI The general solution is given by X (t) = ci where V2. |and 21 >A2 =| ; vi = and v2 (b) Draw a direction field and a phase portrait. Describe the behavior of the solutions as t - o. 1) If the initial condition is a multiple of...
Problem 3. Consider the initial value problem w y sin() 0 Convert the system into a single 3rd order equation and solve resulting initial value problem via Laplace transform method. Express your answer in terms of w,y, z. Problem 4 Solve the above problem by applying Laplace transform to the whole system without transferring it to a single equation. Do you get the same answer as in problem1? (Hint: Denote W(s), Y (s), Z(s) to be Laplace transforms of w(t),...
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