1. Determine the type of the equilibrium point o and plot the phase portraits of the following sy...
5.4 Equilibrium Solutions and Phase Portraits 1. 2 3 3 2 . (a) Draw direction field. Use the points: (0,0), (+1,0), (0, +1), (+1, +1). (b) Draw the phase portrait. (c) Classify the equilibrium solution with its stability. 11 and 2. Suppose 2 x 2 matrix A has eigenvalues – 3 and -1 with eigenvectors respectively. (a) Find the general solution of 7' = A. (b) Draw the phase portrait. (C) Classify the equilibrium solution with its stability. 3. Suppose...
Sketch the phase portraits for the following systems. (Here r and θ are polar coordinates in the plane.) a. r' = r3 - 4r θ' = 1 b. r' = r(1 - r2)(9 - r2) θ' = 1 c. r' = r(1 - r2)(4 - r2) θ' = 2 - r2
1. (This is problem 5 from the second assignment sheet, reprinted here.) Consider the nonlinear system a. Sketch the ulllines and indicate in your sketch the direction of the vector field in each of the regions b. Linearize the system around the equilibrium point, and use your result to classify the type of the c. Use the information from parts a and b to sketch the phase portrait of the system. 2. Sketch the phase portraits for the following systems...
Solve and draw phase portraits. I understand how to
solve but not how to draw, so phase portraits, please.
23 31 IL 9-9 | | 21 47 31 2 1- .) 31 76 73 56
23 31 IL 9-9 | | 21 47 31 2 1- .) 31 76 73 56
1. (20 points) Let
(a) Determine and plot the equilibrium points and nullclines of
the system.
(b) Show the direction of the vector field between the
nullclines
(c) Sketch some solution curves starting near, but not on, the
equilibrium point(s).
(d) Label each equilibrium point as stable or unstable depending on
the behavior of the
solutions nearby, and describe the long-term behavior of all of the
solutions.
#20 please and specifically c.) .... but with the initial
conditions only being A= (1,-1) and D=(-1,2). For A, I got
x(t)=e^(-4t) and y(t) = -e^(-4t). For D, I got x(t)=
3/4*e^(4t)-7/4*e^(-4t) and y(t)=1/4*e^(4t)+7/4*e^(-4t)
295 3.3 Phase Portraits for Linear Systems with Real Eigenvalues 20. The slope field for the system y 3 dx =2x +6y dt dy = 2x - 2y dt is shown to the right. (a) Determine the type of the equilibrium point at the origin. x...
Consider the following magnitude and phase plot of a minimum
phase system. Please answer the following and explain.
Consider the following magnitude and phase plot of a minimum phase system. Is this system stable or unstable? Explain your answer. Bode Diagram: Minimum-Phase Systenm 100 Gain Crossover 40 -60 80 100 90 135 -180 225 -270 -360 Phase Crossover Op Og Frequency (rad/sec)
Consider the following magnitude and phase plot of a minimum phase system. Is this system stable or unstable?...
Determine and plot the magnitude and phase spectra of the
following signal:
please do this by hand, no matlab.
Determine and plot the magnitude and phase spectra of the following signals:
4s +1 2s2 +13s 20 H(s) = 1- Use MATLAB to plot the magnitude and phase responses of this filter. Label 2- What is the type of this filter type (lowpass, highpass, bandpass,.. .? Plcase 3- Derive the partial fraction expansion of H(s) using the residue command in 4- Determine the impulse response h(t) of the system and plot it using MATLAB. the axes completely. explain. MATLAB and write the expression.
Consider the 2-dimensional system of linear equations -2 X' = 2 Note that the coefficient matrix for this system contains a parameter a. (a) Determine the eigenvalues of the system in terms of a (b) The qualitative behavior of the solutions depends value ao where the qualitative behavior changes. Classify the equilibrium point of the system (by type and stability) when a < ao, when a = a), and when a > ao. on the value of a. Determine a...