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Examine the ode system: YO)-Py0+9), where yto-J .P-21P22 y1t)p11 p12 With the following...
2. (28 marks) This questions is about the following system of equations x = (2-x)(y-1) (a) Find all equilibrium solutio...
2. (28 marks) This questions is about the following system of equations x = (2-x)(y-1) (a) Find all equilibrium solutions and determine their type (e.g., spiral source, saddle) Hint: you should find three equilibria. b) For each of the equilibria you found in part (a), draw a phase portrait showing the behaviour of solutions near that equilibrium. -2 (c) Find the nullclines for the system and sketch them on the answer sheet provided. Show the direction of the vector field...
please type your answer or write your answer neatly! 6. Recall that a second order linear...
please type your answer or write your answer neatly!
6. Recall that a second order linear differential equation has the form y" + p(x)y' + g(x)y = g(x), and that initial conditions for such an equation take the form y(20) = yo, y'(x0) = yo, where to, yo, and % are real numbers. (a) State carefully the fundamental existence and uniqueness theorem for such differ- ential equations. (Note: There are many equivalent ways to say the same thing. You need...
A system is modeled by the following LTI ODE: ä(t) +5.1640.j(t) + 106.6667x(t) = u(t) where...
A system is modeled by the following LTI ODE: ä(t) +5.1640.j(t) + 106.6667x(t) = u(t) where u(t) is the input, and the outputs yı(t) and yz(t) are given by yı(t) = x(t) – 2:i(t), yz(t) = 5ä(t) 1. Find the system's characteristic equation 2. Find the system's damping ratio, natural frequency, and settling time 3. Find the system's homogeneous solution, x(t), if x(0) = 0 and i(0) = 1 4. Find ALL system transfer function(s) 5. Find the pole(s) (if...
Please help me complete this problem!!! Thank you and please write neatly!!! (c) Consider the following general second order linear initial value problem with linear variable coefficient:s (at +bi)y&...
Please help me complete this problem!!! Thank you and please
write neatly!!!
(c) Consider the following general second order linear initial value problem with linear variable coefficient:s (at +bi)y"+(at +b'+(ast+bs)y 0, y(0) (00 Use the Laplace Transform to find the ODE that is satisfied by Y(s) y(t)s). What is the order of the new equation? What can you say about the solution to this equation? What can you say about the solution to the original equation?
(c) Consider the following...
Please show all the steps, Thank you! Find yol(t), the zero-input component of the response for an LTIC system described by the following differential equation: (D2 + 6D +9)y(t) (3D+5)r(t) where the i...
Please show all the steps, Thank you!
Find yol(t), the zero-input component of the response for an LTIC system described by the following differential equation: (D2 + 6D +9)y(t) (3D+5)r(t) where the initial conditions are yo(0)-3)0(0) -7
Find yol(t), the zero-input component of the response for an LTIC system described by the following differential equation: (D2 + 6D +9)y(t) (3D+5)r(t) where the initial conditions are yo(0)-3)0(0) -7
Question 1 (42 p) Consider a closed economy where goods market and finalcial markets can be descr...
Question 1 (42 p) Consider a closed economy where goods market and finalcial markets can be described by the following equations for period t С,-100 + 0.5yo- 2000.25Y- 200r G- 100: T-200 Suppose inflation escpectations in this economy is based on past period's inflation rate, ie. Let Yo- FIN)-No the labor force is given as constant at LF- 1000. (4p) Write down the IS equation for this economy (4p) Assume a horizontal LM function where the Central Bank announces the...
I need help with question 30d 16. y = 0 (that is, y(x) = 0 for...
I need help with question 30d
16. y = 0 (that is, y(x) = 0 for all x, also written y(x) = 0) is a solution of (2) (not of (1) if (x) • o , called the trivial solution 17. The sum of a solution of (1) and a solution of (2) is a solution of (1). 18. The difference of two solutions of (1) is a solution of (2). 19. If yı is a solution of (1), what...
5. Consider the following time-dependent Lagrangian for a system with one degree of freedom , (10)...
5. Consider the following time-dependent Lagrangian for a system with one degree of freedom , (10) where 8, m and k are fixed real constants greater than zero. (total 10 points) (a) Write down the Euler-Lagrange equation of motion for this system, and interpret the resulting equation in terms of a known physical system. (1 point) (b) Find Hamiltonian via Legendre transformation. (1 point) (c) Show that q(t) and the corresponding canonical momentum p(t) can be found as follows for...
help me with this. Im done with task 1 and on the way to do task...
help me with this. Im done with task 1 and on the way to do task
2. but I don't know how to do it. I attach 2 file function of rksys
and ode45 ( the first is rksys and second is ode 45) . thank for
your help
Consider the spring-mass damper that can be used to model many dynamic systems -- ----- ------- m Applying Newton's Second Law to a free-body diagram of the mass m yields the...
3.7 Underdamped free vibrations (e.g. a vibrating beam or slinky in damp air A system whose...
3.7 Underdamped free vibrations (e.g. a vibrating beam or slinky in damp air A system whose response is governed by the following constant-coefficient, is performing underdamped free vibrations if oc 1 (underdamped ). (Seetion 6.7). linear, 2td order, ODE ) and 1t)- (freei (a) After assuming a solution t)et where C and p are conustants, show every step that proves yit) can be expressed in terms of the yet-to-be-determined constants A and B and he constant wa (defined above) called...
2. (28 marks) This questions is about the following system of equations x = (2-x)(y-1) (a) Find all equilibrium solutions and determine their type (e.g., spiral source, saddle) Hint: you should find three equilibria. b) For each of the equilibria you found in part (a), draw a phase portrait showing the behaviour of solutions near that equilibrium. -2 (c) Find the nullclines for the system and sketch them on the answer sheet provided. Show the direction of the vector field...
please type your answer or write your answer neatly!
6. Recall that a second order linear differential equation has the form y" + p(x)y' + g(x)y = g(x), and that initial conditions for such an equation take the form y(20) = yo, y'(x0) = yo, where to, yo, and % are real numbers. (a) State carefully the fundamental existence and uniqueness theorem for such differ- ential equations. (Note: There are many equivalent ways to say the same thing. You need...
A system is modeled by the following LTI ODE: ä(t) +5.1640.j(t) + 106.6667x(t) = u(t) where u(t) is the input, and the outputs yı(t) and yz(t) are given by yı(t) = x(t) – 2:i(t), yz(t) = 5ä(t) 1. Find the system's characteristic equation 2. Find the system's damping ratio, natural frequency, and settling time 3. Find the system's homogeneous solution, x(t), if x(0) = 0 and i(0) = 1 4. Find ALL system transfer function(s) 5. Find the pole(s) (if...
Please help me complete this problem!!! Thank you and please
write neatly!!!
(c) Consider the following general second order linear initial value problem with linear variable coefficient:s (at +bi)y"+(at +b'+(ast+bs)y 0, y(0) (00 Use the Laplace Transform to find the ODE that is satisfied by Y(s) y(t)s). What is the order of the new equation? What can you say about the solution to this equation? What can you say about the solution to the original equation?
(c) Consider the following...
Please show all the steps, Thank you!
Find yol(t), the zero-input component of the response for an LTIC system described by the following differential equation: (D2 + 6D +9)y(t) (3D+5)r(t) where the initial conditions are yo(0)-3)0(0) -7
Find yol(t), the zero-input component of the response for an LTIC system described by the following differential equation: (D2 + 6D +9)y(t) (3D+5)r(t) where the initial conditions are yo(0)-3)0(0) -7
Question 1 (42 p) Consider a closed economy where goods market and finalcial markets can be described by the following equations for period t С,-100 + 0.5yo- 2000.25Y- 200r G- 100: T-200 Suppose inflation escpectations in this economy is based on past period's inflation rate, ie. Let Yo- FIN)-No the labor force is given as constant at LF- 1000. (4p) Write down the IS equation for this economy (4p) Assume a horizontal LM function where the Central Bank announces the...
I need help with question 30d
16. y = 0 (that is, y(x) = 0 for all x, also written y(x) = 0) is a solution of (2) (not of (1) if (x) • o , called the trivial solution 17. The sum of a solution of (1) and a solution of (2) is a solution of (1). 18. The difference of two solutions of (1) is a solution of (2). 19. If yı is a solution of (1), what...
5. Consider the following time-dependent Lagrangian for a system with one degree of freedom , (10) where 8, m and k are fixed real constants greater than zero. (total 10 points) (a) Write down the Euler-Lagrange equation of motion for this system, and interpret the resulting equation in terms of a known physical system. (1 point) (b) Find Hamiltonian via Legendre transformation. (1 point) (c) Show that q(t) and the corresponding canonical momentum p(t) can be found as follows for...
help me with this. Im done with task 1 and on the way to do task
2. but I don't know how to do it. I attach 2 file function of rksys
and ode45 ( the first is rksys and second is ode 45) . thank for
your help
Consider the spring-mass damper that can be used to model many dynamic systems -- ----- ------- m Applying Newton's Second Law to a free-body diagram of the mass m yields the...
3.7 Underdamped free vibrations (e.g. a vibrating beam or slinky in damp air A system whose response is governed by the following constant-coefficient, is performing underdamped free vibrations if oc 1 (underdamped ). (Seetion 6.7). linear, 2td order, ODE ) and 1t)- (freei (a) After assuming a solution t)et where C and p are conustants, show every step that proves yit) can be expressed in terms of the yet-to-be-determined constants A and B and he constant wa (defined above) called...
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