please do a and b 4. For the system below a. Show that the system is...
Please show all work if possible, thanks! Show that the system of differential equations is Hamiltonian, and find a Hamiltonian function H(x,y). You may assume that H(0,0) = 0. 3y2 - 2.c dx dt dy dt 6x2 + 2y
1. (Hamilton System) Show that the system a a12yAr2 - 2BxyCy? (1) a1yDx- 2 Ary By2 + is a Hamiltonian system, i.e. find the Hamiltonian function H(r, y) for this system
For the Hamiltonian syste m we did in class: 2. 3 Ic (1) Show that it's a Hamiltonian system with a Hamiltonian function (2) Show that for each c > 0, {(z,y) є R2 . H(z,y) c} is a bounded invariant set of the dynamical system (in fact, it's also closed) (3) Find all the equilibria of this system. Show that H-() is made up of one equilibium point and two homoclinic orbits attached to it. (4) Sketch the invariant...
please show all work thank you 2. (4 points each) In the space provided, take the derivative of each of the following functions. Make sure to use the appropriate notation for the derivative of the given function. (a) y = sin(x2 – 7) (b) y = (cos x)(tan x) (c) g(x) = (d) G(x) = sin? (720) 3х (e) y = x2 (f) F(p) = (1 – 4p2)3 (g) y = [arctan(t)][In(5t)] – 4 (h) f(x) = V5x3 – 7x...
Please do h) and i). The answers have to match (show 3 or 4 answers for each to show that they match I do not need 50). + a D b 1. Consider the signal flow diagram representing a r/n)- y[n] discrete-time LTI system as shown, with a = 0.9 and b= -0.2. Assume initial rest conditions. In each case, explain your work. D a. (1 mark) Show that the difference equation for this system is y[n] – a •y[n...
Please do b and d. The result for 26.5 a is below 26.6. Using the results from exercise 26.5 a, find the solution to y" + 4y fo with y(0) = 0 and y'(0) = 0 for each of the following choices of /: a. fo = 1 b. - 1 d. f(1) = sin(21) e. f(1) = sin(a) where a #2 c. / (0) = 1 26.5 a. C[SOL {[y" + 4y]. [Y'). + 4L[y]1, → = F(s) [s?Y(s)...
Langrange function of a dynamic system is given below, a, b, k1 and k2 are constants. a) Find the Hamiltonian function of the system? b) Determine the Hamiltonian equations of motion for this system? c) Find conservative values, if any? 2 2 Х. L xi 2 a bx 2 2 Х. L xi 2 a bx
4 Consider the system represented in state variable form 0 x+ 2 y [1-1x +[0]u B C(sl- A) Show that a transfer function is related to the state equation by H(s) a) D, and find the transfer function for the system above. (5 marks) Sketch the Bode plot. b) (5 marks) 4 Consider the system represented in state variable form 0 x+ 2 y [1-1x +[0]u B C(sl- A) Show that a transfer function is related to the state equation...
Please solve the following and show steps clearly 1-a casual LTI system is characterized by the following difference equation y[n]-3/4 y[n-1]+1/8 y[n-2]= 2 x[n] find the impulse response, h[n], of this system 2-then find the response of the system to input x[n]= (1/4)^n u[n]
PLEASE WRITE AS CLEAR AS POSSIBLE 5. A quantum system is described by the one-dimensional Hamiltonian (in units here 1) d2 dz2 Notice that this Hamiltonian has the potential energy of x2 (we will soon see that this Hamil tonian describes a good model of molecular vibration). Let us consider the two wavefunctions (a) Show that h(z) and 2(z) are eigenfunctions of this Hamiltonian and find their corre- sponding eigenvalues. (b) Find the constants Ai and A2 that normalize the...