(c) Find a particular solution curve Xp for the linear system cOs t X+ 2 sin...
2. A dragon is flying around in a pattern given by the parametric curve r(t) (cos(t) cos((sin(t) sin(t) cos(t)j. cos(t) - cos sin(t)-sin(t) cos(t))j (a) Find a formula for the velocity of the dragon at time t (b) Find all the times at which the dragon's speed is zero. Explain your reasoning. c) Does the path of the dragon contain any cusps? Explain your reasoning
2. A dragon is flying around in a pattern given by the parametric curve r(t)...
Apply the method of undetermined coefficients to find a
particular solution to the following system.
Apply the method of undetermined coefficients to find a particular solution to the following system. x' = x - 5y + 4 cos 2t, y' = x - y Xp(t) = 0
the solution need to be in terms of sin and cos
(1 point) Consider the linear system -3 -2 = r. 5 3 Find the eigenvalues and eigenvectors for the coefficient matrix. 1 11 = -I V1 = help (numbers) help (matrices) -(3-1)/2 and 1 12 = -. help (numbers) help (matrices) 1 V2 = -(3+i)/2 Find the real-valued solution to the initial value problem x1 = -321 – 2x2, x = 5x1 + 3x2, x1(0) = 2, x2(0) =...
(30 pts) Consider the following sampling system where the input is x(t) = sin 2nt + cos 3nt r(t) Cp (t) (a) (10 pts) Find and plot the Fourier Transform of x(t) (b) (10 pts) What is the Nyquist frequency and period for sampling? (c) (10 pts) Find and plot the Fourier Transform of xp(t) using the Nyquist rate.
(30 pts) Consider the following sampling system where the input is x(t) = sin 2nt + cos 3nt r(t) Cp (t)...
Use the variation of parameters formula to find a general solution of the system x'(t) = Ax(t) + f(t), where A and f(t) are given. 2 A= -4 2 ,f(t) = -1 14 +2t - 1 Let x(t) = x (t) + X(t), where xn(t) is the general solution corresponding to the homogeneous system, 1 xp (t) is a particular solution to the nonhomogeneous system. Find xh (t) and xp(t). and 1 -2 Xh(t) = 41 2 1 1 X(t)...
Use the variation of parameters formula to find a general solution of the system x' (t) = Ax(t) + f(t), where A and f(t) are given. 4 - 1 4 + 4t Let x(t) = xn (t) + xp (t), where xn (t) is the general solution corresponding to the homogeneous system, and xo(t) is a particular solution to the nonhomogeneous system. Find Xh(t) and xp(t). Xh(t) = U. Xp(t) = 0
Marks 4 3. Find the length of the curve x t + cos t, y= t - sin t on the interval 0<t<2m.
Marks 4 3. Find the length of the curve x t + cos t, y= t - sin t on the interval 0
2 2 X Questions 17 and 18 will deal with the linear system X' = - 2 3 pts Question 17 What are the eigenvalues to the linear system? Select the correct answer O 0,-4 O 2,2 O-2 2i 0,4 O 22i 4 pts Question 18 The solution of the linear system is Select the correct answer O None of the above (C X ce2 sin(2t) e cos(2t) 1 cos(2t) 0 sin(2t) 1 25 X c1e -2t sin(t) ce' cost...
Please explain, thank you.
Show that the curve x = 5 cos t, y = 2 sin tcos t has two tangents at (0, 0) and find their equations (smaller slope) (larger slope)
Show that the curve x = 5 cos t, y = 2 sin tcos t has two tangents at (0, 0) and find their equations (smaller slope) (larger slope)
4. Consider the nonhomogeneous linear system of differential equations / 4 3 4t / cos(3t) + 2te4t / l - sin(3t) / + 4tºe4t / sin(3t)) 43.4t sin(3) ( cos(3t) ) Given a particular solution t²4t / t th 4t / Find the general solution of the nonhomogeneous system. Hint: det(A – XI) = 12 – 81 + 25.