![(a) Find all the critical points, and investigate their (linear) stability, as the param eters β and δ are varied. [3 marks]](http://img.homeworklib.com/images/b0bd9204-5dec-4ad2-8088-67eb1d5da6a2.png?x-oss-process=image/resize,w_560)
(a) Find all the critical points, and investigate their (linear) stability, as the param eters β and δ are varied. [3 marks] (b) For this part, set 0. Show that the v axis is invariant. Find the phase flow on this invariant axis. 1 marks
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dt dt (a) Find all the critical points, and investigate their (linear) stability, as the param eters β and δ are varied. [3 marks] (b) For this part, set 0. Show that the v axis is invariant. Fin...
PLEASE HELP !!!! thanks 14. 12 points! The phase portrait (without arrows) of a non-linear syster dz 3-32, 16r dt 2 dy dt a) Mark all critical points directly on the 2 diagram, and classify them...
PLEASE HELP !!!! thanks
14. 12 points! The phase portrait (without arrows) of a non-linear syster dz 3-32, 16r dt 2 dy dt a) Mark all critical points directly on the 2 diagram, and classify them using only the fact that this is a Hamiltonian system. -2 b) Find a Hamitonian function (or conserved quantity) H(,u) whose level curves include the curves shown above.
14. 12 points! The phase portrait (without arrows) of a non-linear syster dz 3-32, 16r dt...
7 marks (4 marks) (3 marks) (a) Is the operator P(v) y'+2ty linear? (Show workings) (b) Find the ...
please answer question 1) to 3) fully step by step
7 marks (4 marks) (3 marks) (a) Is the operator P(v) y'+2ty linear? (Show workings) (b) Find the null space of the operator in (a) above. Question 2 5 marks Let P be a linear operator. Suppose that y is a particular solution to the equation Ply) = b. Prove that any solution to this equation can be written as y = Yo + yi for yo au clement of...
1 Sec. 8.1 8.2 Homework For each of the following systems, find all critical points (b)...
1
Sec. 8.1 8.2 Homework For each of the following systems, find all critical points (b) find the linearization at each critical point and determine the type and stability of each critical point (c) draw a phase portrait confirming the type and stability of all critical points (1) / - (2+)(y-*) V = (4-1)y + r) (2) 1-1- (4) 2 - 1 - ry (5) x = (1-1-y) V-(3--20) Bonus computational work (use technology!) 1. Uee pplane to plot the...
3. Find all critical points of dt dt with the constraint PP = 8 0 (c and boundary conditions x(0) - 0, x(1)- 3. Hint: Write the Euler Lagrange equation (there is no dependence on t), and then use the...
3. Find all critical points of dt dt with the constraint PP = 8 0 (c and boundary conditions x(0) - 0, x(1)- 3. Hint: Write the Euler Lagrange equation (there is no dependence on t), and then use the boundary conditions and the constraint to reach a system of 2 equations (with quadratic terms) of two unknown constants a, b Solve it by first finding a quadratic equation for a/b
3. Find all critical points of dt dt with...
4 Consider the autonomous differential equation y f(v) a) (3 points) Find all the equilibrium solutions (critical...
4 Consider the autonomous differential equation y f(v) a) (3 points) Find all the equilibrium solutions (critical points). b) (3 points) Use the sign of y f(z) to determine where solutions are increasing / decreasing. Sketch several solution curves in each region determined by the critical points in c) (3 points) the ty-plane. d) (3 points) Classify each equilibrium point as asymptotically stable, unstable, or semi-stable and draw the corresponding phase line.
4 Consider the autonomous differential equation y f(v)...
12. Find all the equilibrium points of the competing species model [2.5 marks] x' = 0.6-0.2x2-0....
12. Find all the equilibrium points of the competing species model [2.5 marks] x' = 0.6-0.2x2-0. Iy 13. Select the second-order equation "+9xy+6y 2x2 written as a system of first-order 2.5 marks] equations a) u'=v' b) uv u'=v v'=-9xv-би-2x2 d) v d) 4xy 14. Consider the differential equation given by y a) On the axis provided below, sketch a slope field for the given differential equation at the five points indicated by a circle. 2 marks] b) Use Euler's method...
Answer for part b is R=247 and V=16v 50. (8 points) You set up the circuit...
Answer for part b is R=247
and V=16v
50. (8 points) You set up the circuit shown below, C = 5.00 uF. At the time t = 0, you close the switch and then measure the charge q on the capacitor a function of the current i through the resistor. A graph of your results is also shown below. 60.00 50.00 q=-1.2475*1 + 79.9 R2 = 0.9999 40.00 Switch closed 30.00 20.00 10.00 60 i VA +q - 0.00 0...
How to do question B 2,3,4,5? 3. a) Find the solution v ote ordinary diferetinl equation with the initial coditions: b)...
How to do question B
2,3,4,5?
3. a) Find the solution v ote ordinary diferetinl equation with the initial coditions: b) i) Recast our third ord ODE into a system af first order ODEs af the formA.v, where v' = dv/dz f(v) and v = (y, y,y")". You should show all working to find the corresponding matrix A. Do not solve the system. 4 mark Solve it only by hand and show your complete work. Do not use a calculator...
NOTE: PLEASE DO Q.3 Part d and e Answers are given below: Question 3 (16 marks)...
NOTE: PLEASE DO Q.3 Part d and e
Answers are given below:
Question 3 (16 marks) Consider the periodic signal T v(t)24 cos(2t ) - 4 sin(5t - 2 The signal v is given as an input to a linear time-invariant continuous-time system with fre- quency response 4 0 lwl 2 2 jw H(w) lwlT 2, 1 2 jw (a) 3 marks] Find the fundamental period To and frequency wo of v (b) [3 marks] Express v in cosine sine...
2 dv do sine Math 2120 Spring 2019 Final Exam Show Works fo NAME #1 Give a set of parametric equations that describes the following curves. The piecewise linear path from P(-2.3) to 0(2.-3) to R...
2
dv do sine Math 2120 Spring 2019 Final Exam Show Works fo NAME #1 Give a set of parametric equations that describes the following curves. The piecewise linear path from P(-2.3) to 0(2.-3) to R(3.5). using parameter values Osis2 #2. Find the points at which the following polar curves have a horizontal or a vertical tange #3. Find an Equation for describing the following object: A sphere with center (1, 2,0 pa point (3, 4, 5). dy Slopes of...
PLEASE HELP !!!! thanks
14. 12 points! The phase portrait (without arrows) of a non-linear syster dz 3-32, 16r dt 2 dy dt a) Mark all critical points directly on the 2 diagram, and classify them using only the fact that this is a Hamiltonian system. -2 b) Find a Hamitonian function (or conserved quantity) H(,u) whose level curves include the curves shown above.
14. 12 points! The phase portrait (without arrows) of a non-linear syster dz 3-32, 16r dt...
please answer question 1) to 3) fully step by step
7 marks (4 marks) (3 marks) (a) Is the operator P(v) y'+2ty linear? (Show workings) (b) Find the null space of the operator in (a) above. Question 2 5 marks Let P be a linear operator. Suppose that y is a particular solution to the equation Ply) = b. Prove that any solution to this equation can be written as y = Yo + yi for yo au clement of...
1
Sec. 8.1 8.2 Homework For each of the following systems, find all critical points (b) find the linearization at each critical point and determine the type and stability of each critical point (c) draw a phase portrait confirming the type and stability of all critical points (1) / - (2+)(y-*) V = (4-1)y + r) (2) 1-1- (4) 2 - 1 - ry (5) x = (1-1-y) V-(3--20) Bonus computational work (use technology!) 1. Uee pplane to plot the...
3. Find all critical points of dt dt with the constraint PP = 8 0 (c and boundary conditions x(0) - 0, x(1)- 3. Hint: Write the Euler Lagrange equation (there is no dependence on t), and then use the boundary conditions and the constraint to reach a system of 2 equations (with quadratic terms) of two unknown constants a, b Solve it by first finding a quadratic equation for a/b
3. Find all critical points of dt dt with...
4 Consider the autonomous differential equation y f(v) a) (3 points) Find all the equilibrium solutions (critical points). b) (3 points) Use the sign of y f(z) to determine where solutions are increasing / decreasing. Sketch several solution curves in each region determined by the critical points in c) (3 points) the ty-plane. d) (3 points) Classify each equilibrium point as asymptotically stable, unstable, or semi-stable and draw the corresponding phase line.
4 Consider the autonomous differential equation y f(v)...
12. Find all the equilibrium points of the competing species model [2.5 marks] x' = 0.6-0.2x2-0. Iy 13. Select the second-order equation "+9xy+6y 2x2 written as a system of first-order 2.5 marks] equations a) u'=v' b) uv u'=v v'=-9xv-би-2x2 d) v d) 4xy 14. Consider the differential equation given by y a) On the axis provided below, sketch a slope field for the given differential equation at the five points indicated by a circle. 2 marks] b) Use Euler's method...
Answer for part b is R=247
and V=16v
50. (8 points) You set up the circuit shown below, C = 5.00 uF. At the time t = 0, you close the switch and then measure the charge q on the capacitor a function of the current i through the resistor. A graph of your results is also shown below. 60.00 50.00 q=-1.2475*1 + 79.9 R2 = 0.9999 40.00 Switch closed 30.00 20.00 10.00 60 i VA +q - 0.00 0...
How to do question B
2,3,4,5?
3. a) Find the solution v ote ordinary diferetinl equation with the initial coditions: b) i) Recast our third ord ODE into a system af first order ODEs af the formA.v, where v' = dv/dz f(v) and v = (y, y,y")". You should show all working to find the corresponding matrix A. Do not solve the system. 4 mark Solve it only by hand and show your complete work. Do not use a calculator...
NOTE: PLEASE DO Q.3 Part d and e
Answers are given below:
Question 3 (16 marks) Consider the periodic signal T v(t)24 cos(2t ) - 4 sin(5t - 2 The signal v is given as an input to a linear time-invariant continuous-time system with fre- quency response 4 0 lwl 2 2 jw H(w) lwlT 2, 1 2 jw (a) 3 marks] Find the fundamental period To and frequency wo of v (b) [3 marks] Express v in cosine sine...
2
dv do sine Math 2120 Spring 2019 Final Exam Show Works fo NAME #1 Give a set of parametric equations that describes the following curves. The piecewise linear path from P(-2.3) to 0(2.-3) to R(3.5). using parameter values Osis2 #2. Find the points at which the following polar curves have a horizontal or a vertical tange #3. Find an Equation for describing the following object: A sphere with center (1, 2,0 pa point (3, 4, 5). dy Slopes of...
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