Problem 4. (6 pts) L,V/,(0,φ) ? e result of part (a), to determine Y,"(0.9) , up...
Consider the function y(φ)-e",-ie h2 d where I is a constant? If so, what is the a) Is it an eigenfunctions of the operator O-- eigenvalue? (answer: no) b) Normalize the function on the domain 0 φś2π (in this case, normalization implies | | ψ(0) 12 dφ= 1 ). Euler's identity, etimp-cos(mo) ± isin(mo), where m is a constant, will be useful (φ)-F(e"-ie")) to evaluate the normalization constant. (answer: ya normalized Consider the function y(φ)-e",-ie h2 d where I is...
Problem 1 part II and Problem 2 part I and II Problem 1: (Short Answer) 6 pts] The region R is bounded by y 0, 0, 2, and y- 2 4 1, 3 pts] If R is revolved about the line x = 5. If an integral or sunn of integrals with respect to z is used to calculate the volume, explain whether the washer or shell method should be used II. 3 pts) Suppose that R is the base...
Consider the general sinusoidal function y(t)-Asin (wt + φ). Part a If A-1 and y(0)-1, what is φ? (Please state as a decimal answer, eg. 0.1 π-meaning add the zero in front) Enter answer here 0 of 6 attempts used CHECK ANSWER Part b If A-1 and y(0)-0.5, what is φ? Select the correct answer O 30 π Part c If y(t) describes the position with time, what is the proper formula for velocity with time? (Recall velocity is related...
Problem 3 6 pts] The region R bounded by y V, y 0, and 4 is revolved about the line y3 Calculate the volume of the solid using the washer method and simplify your final answer. -3 Problem 4: 8 pts] The region R is boud by y2 and y 8- 2 I. Set up, but do not evaluate, an integral or sum of integrals that would give the volume of the solid of revolution formed when R is revolved...
Problem 2: (40 pts) Part A: (20pts) A third-order system has an of Y(s)-L[y(t) corresponding to a unit step input u(t) is known to be input of u(t) and an output of y(t). The forced response portion 1 Ys) (3 +3s2+ 4s +5) = a) Determine the input-output differential equation for the system b) From your result in a), determine the transformed free response Yee (s) corresponding to initial conditions of: y(0)= y(0) = 0 and ý(0)-6 Part B (20pts)...
* Let φ : R3-+ R be a continuous function. The level sets of φ are the sets 4:-{(z, y, z) e R3 Id(z, y, z) =c); where c is a real constant (c) Use the setup in this problem to argue that a sequence on the unit sphere x E R31 (- is the standard Euclidean norm) cannot converge to a point that is not an element of the unit sphere. * Let φ : R3-+ R be a...
¥(r,0,) = e-6 to determine the ground state energy of the hydrogen atom. In the equation, b is the parameter to be varied. Hint: Use Schrödinger's equation in spherical coordinates and calculate the normalization constant first. Make use of the symmetries!
only do problem 3a,b. show full work Problem 2 (20 pts). The function V (x, y, z) = 7.,3,2)yt Calculate v. 1,2+22 C Problem 3 (20 pts). Considering the function V of problem 2, (a) Show that V can be written in spherical coordinates as V(r, θ, φ)-1 (10 pts) (b) The gradient of a function in spherical coordinates is ▽V = r + θ + φ 1 a Calculate the gradient of V in spherical coordinates. (5 pts)
Review Part A What is the angle φ between vectors E and F n the figure? (Figure 1) Submit gure Part B Use components to determine the magnitude of G-B+ Submit Part Part C Use components to determine the direction of G-E+F 0- counterclockwise from the positive z-axis Submit Request Answer Provide Feedback
#4 Problem 1 Find the general solution for the given differential equation Problem 2 Solve the d.e. y(4)2y(3) +2y() 3et +2te- +e-sint. Problem 3 Determine the second, third and fourth derivative of φ(zo) for the given point xo if y = φ(z) is a solution of the given initial-value problem. ·ry(2) + (1 +z?)y(1) + 31n2(y) = 0; y(1) = 2, y(1)(1)-0 yay) + sina()0: y(0)()a Problem 4 Using power series method provide solution for the d.e. Problem 5 Using...