Inhomogeneous and polar probs: Problem 6 Previous Problem Problem List Next Problem (1 point) A c...
(15 pts) Bessel functions and the vibration of a circular drum In polar coordinates, the Laplacian is just like the Laplacian for the cylinder, but with the removed part เอ The structure of the Laplacian is what we call separable because the r and 0 terms are separate this allows us to solve certain physics problems on the disc by searching for solutions of the form f(r,0)-ar)b() The vibration of a circular drum head is described by 02t where u...
Section 1.1 Direction Fields: Problem 4 Previous Problem Problem List Next Problem (1 point) A function y(t) satisfies the differential equation dy (a) What are the constant solutions of this equation? Separate your answers by commas (b) For what values of y is y strictly increasing? and liy< Note: You can earn partial credit on this problem. Preview My Answers Suhmit Answers
Homework 5: Problem 9 Next Problem Problem List Previous Problem (1 point) Find the temperature function u(r, t) (where is the position along the rod in cm and t is the time) of a 12 cm rod with conducting constant 0,1 whose endpoint are insulated such that no heat is lost, and whose initial temperature distribution is given by: if 6< <8 4 u (,0) 10 otherwise 0.1 To start, we have L 12 Because the rods are insulated, we...
HW 2.4: Problem 3 Previous Problem Problem List Next Problem (1 point) A Bernoulli differential equation is one of the form + P(x)y -- Q(x)y". Observe that, if n = 0 or 1, the Bemoulli equation is linear. For other values of n the substitution -y transforms the Bernoulli equation into the linear equation + (1 - n)P(x)u = (1 - 1)(a). Use an appropriate substitution to solve the equation and find the solution that satisfies y(1) = 1. Preview...
Section 5.3: Problem 25 Previous Problem Problem List Next Problem (1 point) The velocity function is v(t) = - + 5t – 6 for a particle moving along a line. Find the displacement and the distance traveled by the particle during the time interval (-1,6). displacement = 26.8333333333 distance traveled = 27.166 If needed, see page 287 of the Stewart Essential Calculus textbook for the definitions of these terms.
Sections 11.3-11.4: Problem 1 Previous Problem Problem List Next Problem (1 point) Any point in the plane can be written in polar coordinates (r, @) with – Ž <os For each of the following problems, find polar coordinates with – <03 1 (a) If (x, y) = (16, —8) then (r, 0) =( ), ), ), (b) If (x, y) = (15,2) then (r, 0) =( (c) If (x, y) = (-7, -7) then (r, 0) =( (d) If (x,...
Section 3.7 Free Mechanical Vibrations: Problem 4 Previous Problem Problem List Next Problem (1 point) This problem is an example of critically damped harmonic motion. A mass m = 8 kg is attached to both a spring with spring constant k = 200 N/m and a dash-pot with damping constant c = 80 N s/m The ball is started in motion with initial position zo = 7 m and initial velocity vo = -39 m/s. Determine the position function r(t)...
HW6: Problem 6 Previous Problem Problem List Next Problem (1 point) Find the steady state solution y(x) for the heat problem U = Uxx + 12x +4, 0<x<3, u(0, 1) = 0, u(3, 1) = 0 u(x,0) = 3 sin(x)e Note you do not need to find u(x,t). y(x) =
Section 1.1 Direction Fields: Problem 9 Previous Problem Problem List Next Problem (1 point) Consider the slope field shown (a) For the solution that satisfies y(0) -0, sketch theEBM solution curve and estimate the following: y(1) A and y(-1) (b) For the solution that satisfies y(0) 1, sketch the solution curve and estimate the following: y(0.5) A t and y(-1) (c) For the solution that satisfies y(0) =-1 , sketch the solution curve and estimate the following: and y(-1) Section...
Previous Problem List Next (1 point) The tank in the form of a right-circular cone of radius 4 feet and height 29 feet standing on its end, vertex down, is leaking through a circular hole of radius 2 inches. Assume the friction coefficient to be c = 0.6 and g=32ft/. Then the equation governing the height h of the leaking water dh - seconds to If the tank is initially full, it will take it empty.