Homework Answers
apply laplace transform to get transfer function and use MATLAB
to get PZMAP ..decide the stability of system by using the location
of poles![>>n[9 7 51; >> d-[2 6 3 1]; >>sys-tf (n, d) sys 9 s^2 + 7 s+ 5 2 s 3 6 s 2 + 3 s 1 Continuous-time transfer function >>pzmap](http://img.homeworklib.com/images/1c7a4372-a1cd-4766-9e30-e2c6982bf524.png?x-oss-process=image/resize,w_560)
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For the system described by the following differential equation d3y(t) d2y(t) d2x(t) dy(t) 3 dt dx(t)...
1) Solve The Differential Equation: a) d3y ,d2y dy -y 0 dx dx3 3 3 b)...
1) Solve The Differential Equation: a) d3y ,d2y dy -y 0 dx dx3 3 3 b) dy 6 dx4 ,d2y 5 dx224 dy 36y 0 dx dx3
Q.4) [25 Marks] a) [15] Consider a CT LTI system described by the following differential equation...
Q.4) [25 Marks] a) [15] Consider a CT LTI system described by the following differential equation (assume zero initial conditions): dºy(t) _6dy(t) + 3 dy(t) = 2x(6) dt3-6 dt2 +8 dt = 2x(t) [5] Using Laplace transform and its properties determine the transfer function H(s) [5] Draw the pole-zero diagram of H(s) (5) Write down all possible Region-of-Convergence (ROC) for the H(s) (iii) [5] white b) (10) Determine the signal x(t) ( assume it to be right-sided signal) when the...
No Need to Solve just write it out. dy = 9. Rewrite the given differential equation...
No Need to Solve just write it out.
dy = 9. Rewrite the given differential equation as a first order system in normal form. Express the system in the matrix form ă' = A +F(t), and let x1 = y, x2 day х3 dy 6 + 15y = sint dt3 dt dt dt2 dạy
Problem 3. Consider the following continuous differential equation dx dt = αx − 2xy dy dt...
Problem 3. Consider the following continuous differential equation dx dt = αx − 2xy dy dt = 3xy − y 3a (5 pts): Find the steady states of the system. 3b (15 pts): Linearize the model about each of the fixed points and determine the type of stability. 3b (15 pts): Draw the phase portrait for this system, including nullclines, flow trajectories, and all fixed points. Problem 2 (25 pts): Two-dimensional linear ODEs For the following linear systems, identify the...
(1 point) If the differential equation d2x m 7 dx dt + 8x = 0 dt2...
(1 point) If the differential equation d2x m 7 dx dt + 8x = 0 dt2 is overdamped, the range of values for m is? Your answer will be an interval of numbers given in the form (1,2), (1,2), (-inf,6], etc.
15. A dynamical system is modeled by the following differential equation under zero initial conditions: d’y(t)...
15. A dynamical system is modeled by the following differential equation under zero initial conditions: d’y(t) d’y(t) dy(t) du(t) + 5 + dt4 + 15 dt3 + 2y(t) = 8 + 10u(t) dt2 dt dt d4y(t) Write the system's state equation and the system's output equation.
Find the time constant t of the following differential equation: a(dy/dt)+by+cx=e(dx/dt)+f(dy/dt)...
Find the time constant t of the following differential
equation: a(dy/dt)+by+cx=e(dx/dt)+f(dy/dt)+g, of the given that x
is the inout, y is the output, and a through g are constants.
13, Find the time constant τ from the following differential equation, dt dt given that x is the input, y is the output and, a through g are constants. It is known that for a first-order instrument with differential equation a time constant r- alao dy the
13, Find the time...
7. Solve the following differential equations. dy 2 y= 5x, x>0. + a) dx dx 1+2x 4e', t>0 b) t dt 7....
7. Solve the following differential equations. dy 2 y= 5x, x>0. + a) dx dx 1+2x 4e', t>0 b) t dt
7. Solve the following differential equations. dy 2 y= 5x, x>0. + a) dx dx 1+2x 4e', t>0 b) t dt
(1 point) If the differential equation d2x dt2 . dx + 6- m + 3x =...
(1 point) If the differential equation d2x dt2 . dx + 6- m + 3x = 0 dt is overdamped, the range of values for m is? (inf,3) Your answer will be an interval of numbers given in the form (1,2), (1,2), (-inf,6), etc. (1 point) Write the given second order equation as its equivalent system of first order equations. u" + 3 + 7u = 0 Use v to represent the "velocity function", i.e. V = u(t). Use v...
3. Find the solutions to the following differential equations: [mark 25% d2x dx 5 2x 5...
3. Find the solutions to the following differential equations: [mark 25% d2x dx 5 2x 5 (1) dt2 dt x(0) (0) 0 (2) Use the Final Value Theorem to determine x(t) as t -» co from X(s) Note: Dots denote differentiation with respect to time
3. Find the solutions to the following differential equations: [mark 25% d2x dx 5 2x 5 (1) dt2 dt x(0) (0) 0 (2) Use the Final Value Theorem to determine x(t) as t -» co...
1) Solve The Differential Equation: a) d3y ,d2y dy -y 0 dx dx3 3 3 b) dy 6 dx4 ,d2y 5 dx224 dy 36y 0 dx dx3
Q.4) [25 Marks] a) [15] Consider a CT LTI system described by the following differential equation (assume zero initial conditions): dºy(t) _6dy(t) + 3 dy(t) = 2x(6) dt3-6 dt2 +8 dt = 2x(t) [5] Using Laplace transform and its properties determine the transfer function H(s) [5] Draw the pole-zero diagram of H(s) (5) Write down all possible Region-of-Convergence (ROC) for the H(s) (iii) [5] white b) (10) Determine the signal x(t) ( assume it to be right-sided signal) when the...
No Need to Solve just write it out.
dy = 9. Rewrite the given differential equation as a first order system in normal form. Express the system in the matrix form ă' = A +F(t), and let x1 = y, x2 day х3 dy 6 + 15y = sint dt3 dt dt dt2 dạy
(1 point) If the differential equation d2x m 7 dx dt + 8x = 0 dt2 is overdamped, the range of values for m is? Your answer will be an interval of numbers given in the form (1,2), (1,2), (-inf,6], etc.
15. A dynamical system is modeled by the following differential equation under zero initial conditions: d’y(t) d’y(t) dy(t) du(t) + 5 + dt4 + 15 dt3 + 2y(t) = 8 + 10u(t) dt2 dt dt d4y(t) Write the system's state equation and the system's output equation.
Find the time constant t of the following differential
equation: a(dy/dt)+by+cx=e(dx/dt)+f(dy/dt)+g, of the given that x
is the inout, y is the output, and a through g are constants.
13, Find the time constant τ from the following differential equation, dt dt given that x is the input, y is the output and, a through g are constants. It is known that for a first-order instrument with differential equation a time constant r- alao dy the
13, Find the time...
7. Solve the following differential equations. dy 2 y= 5x, x>0. + a) dx dx 1+2x 4e', t>0 b) t dt
7. Solve the following differential equations. dy 2 y= 5x, x>0. + a) dx dx 1+2x 4e', t>0 b) t dt
(1 point) If the differential equation d2x dt2 . dx + 6- m + 3x = 0 dt is overdamped, the range of values for m is? (inf,3) Your answer will be an interval of numbers given in the form (1,2), (1,2), (-inf,6), etc. (1 point) Write the given second order equation as its equivalent system of first order equations. u" + 3 + 7u = 0 Use v to represent the "velocity function", i.e. V = u(t). Use v...
3. Find the solutions to the following differential equations: [mark 25% d2x dx 5 2x 5 (1) dt2 dt x(0) (0) 0 (2) Use the Final Value Theorem to determine x(t) as t -» co from X(s) Note: Dots denote differentiation with respect to time
3. Find the solutions to the following differential equations: [mark 25% d2x dx 5 2x 5 (1) dt2 dt x(0) (0) 0 (2) Use the Final Value Theorem to determine x(t) as t -» co...
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