9. From the phase-line diagram, sketch a solution starting from the specified initial condition. 11.) start...
Math 155. Homework 5. Section 4.1 1. Use the graph of the rate of change to sketch a graph of the function, starting from the given initial condition (a) Start from z(0) 1 dz dt (b) Start from (0) 10 dw dt 10 -20 30
Math 155. Homework 5. Section 4.1 1. Use the graph of the rate of change to sketch a graph of the function, starting from the given initial condition (a) Start from z(0) 1 dz dt...
1) Given the phase diagram above, calculate: What is the initial
boiling point of a solution with xB= 0.25?
2) Given the phase diagram above, calculate: If fractional
distillation was performed on a solution with xB= 0.25,
what would be the composition of the final distillate?
3) Given the phase diagram above: What is the sign of DH mixing
for the formation of A-B solution?
4) What is the composition of the azeotrope?
0.1 02 03 04 05 06 07...
3) Sketch a phase diagram (temperature vs. average system composition) of an ideal solution of two components A and B. Explain how you can obtain a pure sample of B from this mixture using fractional distillation. Indicate on your phase diagram the purification process you describe in your explanation.
1) Find the general solution of di = Ay where Then sketch the phase portrait in the x-y plane, where Finally, classify the equilibrium solution at the origin as a source, spiral sink, etc. 2) Repeat for the matrix | 3 -31 -2 -2] 3) Repeat for the matrix 4 — 4) Repeat for the matrix [95 -9 15 but you don't need to sketch the phase portrait.
Find the solution to the given system that satisfies the given initial condition. _9_0 -9 x'(t) = 1 2 0 (x(t), 9_0 -5 ܕ (a) x(0)=1 (b) x( -r'- ܝ ܬ . 1 - 4 (a) x(f)- (Use parentheses to clearly denote the argument of each function.)
1) Find the particular solution of the differential equation that satisfies the initial condition. (Enter your solution as an equation.) Differential Equation Initial Condition yy' − 4ex = 0 y(0) = 9 2) Find the particular solution of the differential equation that satisfies the initial condition. (Enter your solution as an equation.) Differential Equation Initial Condition 10xy' − ln(x5) = 0, x > 0 y(1) = 21 Just really confused on how to do these, hope someone can help! :)
16.1 For the following systems, sketch the Bode diagram, and from the straight-line approximations to the gain and phase plots, estimate the maximum value of K for which the system is stable: a. GH(s) = s(s + 1) (s + 4) b. GH(s) = = s(1 + s) KS c. GH() = 6 *21 к d. GH(s) = s(s? + 2s + 16) 5K(1 + s) e. GH(S) = f'( + s/352
Problem 4: [8 Points] x(t) is a continuous periodic signal that has complex exponential Fourier series coefficients as Do = 1, Dn = 2 (1 + j(-1)") Sketch the magnitude and phase spectral-line up to the a) b) Estimate the signal's power from the 1t four h c) Write the math ematical expression for the complex exponential Fourier series expansion form. 12) Solution:
Problem 4: [8 Points] x(t) is a continuous periodic signal that has complex exponential Fourier series coefficients...
(1 point) Suppose 41 yl i(1) = (a) Find ci and c2 (b) Sketch the phase plane trajectory that satisfies the given initial condition. Which graph most closely resembles the graph you drew? B (c) What is the approximate direction of travel for the solution curve, as t increases from -oo to o0? OA. along the line y toward the origin and then along the line y-z away from the origin 41 yl B. along the line y z toward...
ODE
From van der pol’s equation
4. For μ = 1 .5 and the initial conditions x(0) = 0.a and x (0)= 0b , where a and b are before the last and the last digits of your student ID (replace zeros by 9), respectively, use the Euler's method to convince yourself that the trajectory is "attracted" to the closed orbit from question 3 for μ = 1 .5 from inside. Supply the table of the first 20 values of...