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7. Consider the three fundamental linearized equations developed in class: (1) the Equation of Continuity, (2)...
Chapter 7, Section 7.7, Question 07 Consider the following system of equations. (a) Find a fundamental matrix for the g...
Chapter 7, Section 7.7, Question 07 Consider the following system of equations. (a) Find a fundamental matrix for the given system of equations. Use the eigenvectors so that the coefficeints in the first row all equal 1 Equation Editor Ω Common Matrix Ψ (t) = (b) Find the fundamental matrix重(t) satisfying重(0) = 1. Equation Editor Ω Common Matrix tan a) sin(a) 0os(a) 重(t) =
Chapter 7, Section 7.7, Question 07 Consider the following system of equations. (a) Find a fundamental...
#1 The Equation of Continuity: Consider Figure 1 which illustrates a small mathernat ical box in...
#1 The Equation of Continuity: Consider Figure 1 which illustrates a small mathernat ical box in a fluid. The basic idea behind the equation of continuity is that the rate of mass flow into the box must equal the time rate of change of the mass in the box (pur)l Figure 1: A small mathematical box in a fluid A) Consider just the 2-faces of the box for now. Figure 1 shows ρυ.Ε entering at and leaving at + ρ...
Consider the following system of equations. orie 10 x = 5 la (a) Find a fundamental...
Consider the following system of equations. orie 10 x = 5 la (a) Find a fundamental matrix for the given system of equations. (t) = Equation Editor Common 12 Matrix sin(a) cos(a) tan(a) seca) osca) cot(a) de lidz jjar vayalal U s in(a) cos(@) tana ) (b) Find the fundamental matrix (t) satisfying • (0) = I. (t) = Equation Editor Common 2 Matrix cos(a) tan(a) sin(a) seca) sin- (@) sec(a) csele) cot(a) den ſide | saz cos @) tan-(a)
write the state space equation using the following states also write the CCRs , ssrs ,...
write the state space equation using the following
states
also write the CCRs , ssrs , free body diagram
and finally state space equation
Figure 1: Cart-pendulum system. 7. Bonus Marks: Verify that the ODEs given in (1) and (2) model the cart pendulum. The following hints may be useful: (a) You want to largely follow the procedure taught in class. (b) Select a, e, i and 6 as states. List your inputs, CCRs and SSRs. Make sure to write...
d. Show the algebraic steps in deriving equation (5) using equations (1) and (3). Please explain...
d. Show the algebraic steps in deriving equation (5) using
equations (1) and (3).
Please explain this very well.
When a string is stretched between two fixed points, the speed of the waves formed on it is given by the following equation. F (1) V= u Mass of the string per unit length or linear density of the string is given by U= m L (2) Using the general velocity, wavelength and frequency relationship for a wave and considering the...
03:15 points Answer brielly to each of the following questions (a) State the differential form of...
03:15 points Answer brielly to each of the following questions (a) State the differential form of the continuity equation Derive the integral form of the continuity equation from its differential form. Identify all the quantities and indicate the units. () (b) What are the three constitutive relationships to characterize electrical media What is the difference between a linear and a non-linear medium? (2) (c) Starting from the time-harmonic form of Maxwell's equations, derive the wave equation for time- varying magnetic...
Consider the cannon model developed and discussed in class. Using the equations below, a launch speed...
Consider the cannon model developed and discussed in class. Using the equations below, a launch speed of 12 m/s, a launch angle of 57.5o , and g = 9.81 m/s2 , answer the following questions h(t)= vt sinØ -(1/2)gt^2 x(t)= vt cos Ø a. Develop an algorithm to determine the time required to reach a height of at least 2.8 meters. List the steps of the algorithm, do not solve the equations. b. Solve the equations to compute the time...
1.) (a) State Maxwell’s equation for the curl of the magnetic and the electric field in...
1.) (a) State Maxwell’s equation for the curl of the magnetic and the electric field in free space. State the meaning of all the terms in the equations and identify the displacement current density. Using Maxwell’s equations, derive the wave equations for B. Show that the wave equations admit plane waves for the electric and magnetic fields in free space of the form ? = ??? ?(??−??) , ? = ??? ?(??−??) where ?? and ?? are constant vectors with...
= 2. We wish to 7. Consider the differential equation y' + y = 2.. with...
= 2. We wish to 7. Consider the differential equation y' + y = 2.. with the initial conditions y(0) approximate y(1). (a) Set up Euler's method by hand and use it to approximate y(1) with a step size of h = 25. (You may use only a calculator for this question) (b) Use Mathematica to do Euler's method with the step sizes of h= .1,.01, .001, and .0001.
C Consider a differential equation with the given slope field and the in y(0) = 1....
C Consider a differential equation with the given slope field and the in y(0) = 1. 0.5 st -0.5 (a) Explain why, if you wanted to approximate y(2) using two steps of Euler's method, you would need At = 1. (b) Use a straight edge to graph two steps of Euler's method to approximate y(2). (c) This time, instead of using two steps of Euler's method, sketch on the same slope field what it would look like if you used...
Chapter 7, Section 7.7, Question 07 Consider the following system of equations. (a) Find a fundamental matrix for the given system of equations. Use the eigenvectors so that the coefficeints in the first row all equal 1 Equation Editor Ω Common Matrix Ψ (t) = (b) Find the fundamental matrix重(t) satisfying重(0) = 1. Equation Editor Ω Common Matrix tan a) sin(a) 0os(a) 重(t) =
Chapter 7, Section 7.7, Question 07 Consider the following system of equations. (a) Find a fundamental...
#1 The Equation of Continuity: Consider Figure 1 which illustrates a small mathernat ical box in a fluid. The basic idea behind the equation of continuity is that the rate of mass flow into the box must equal the time rate of change of the mass in the box (pur)l Figure 1: A small mathematical box in a fluid A) Consider just the 2-faces of the box for now. Figure 1 shows ρυ.Ε entering at and leaving at + ρ...
Consider the following system of equations. orie 10 x = 5 la (a) Find a fundamental matrix for the given system of equations. (t) = Equation Editor Common 12 Matrix sin(a) cos(a) tan(a) seca) osca) cot(a) de lidz jjar vayalal U s in(a) cos(@) tana ) (b) Find the fundamental matrix (t) satisfying • (0) = I. (t) = Equation Editor Common 2 Matrix cos(a) tan(a) sin(a) seca) sin- (@) sec(a) csele) cot(a) den ſide | saz cos @) tan-(a)
write the state space equation using the following
states
also write the CCRs , ssrs , free body diagram
and finally state space equation
Figure 1: Cart-pendulum system. 7. Bonus Marks: Verify that the ODEs given in (1) and (2) model the cart pendulum. The following hints may be useful: (a) You want to largely follow the procedure taught in class. (b) Select a, e, i and 6 as states. List your inputs, CCRs and SSRs. Make sure to write...
d. Show the algebraic steps in deriving equation (5) using
equations (1) and (3).
Please explain this very well.
When a string is stretched between two fixed points, the speed of the waves formed on it is given by the following equation. F (1) V= u Mass of the string per unit length or linear density of the string is given by U= m L (2) Using the general velocity, wavelength and frequency relationship for a wave and considering the...
03:15 points Answer brielly to each of the following questions (a) State the differential form of the continuity equation Derive the integral form of the continuity equation from its differential form. Identify all the quantities and indicate the units. () (b) What are the three constitutive relationships to characterize electrical media What is the difference between a linear and a non-linear medium? (2) (c) Starting from the time-harmonic form of Maxwell's equations, derive the wave equation for time- varying magnetic...
= 2. We wish to 7. Consider the differential equation y' + y = 2.. with the initial conditions y(0) approximate y(1). (a) Set up Euler's method by hand and use it to approximate y(1) with a step size of h = 25. (You may use only a calculator for this question) (b) Use Mathematica to do Euler's method with the step sizes of h= .1,.01, .001, and .0001.
C Consider a differential equation with the given slope field and the in y(0) = 1. 0.5 st -0.5 (a) Explain why, if you wanted to approximate y(2) using two steps of Euler's method, you would need At = 1. (b) Use a straight edge to graph two steps of Euler's method to approximate y(2). (c) This time, instead of using two steps of Euler's method, sketch on the same slope field what it would look like if you used...
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