Find the general solution of jutt + 2 ut + 2 u 3 u(0,t)ut)-0for all t s o ater for all x E (0, π), t > 0 Be sure to clearly indicate the following steps in your solution: 1. 2. 3. How to use separation of variables How to solve the resulting elgenfuiction/eigenvalue problem How the superposition principle is used.
Problem 3 Convert the following ODE to state space: dv(t) 50v(t)ut) dt 1000 Output of the system y(t) = v(t)
3) [10 pts.] Find the Fourier transform of x(t) = cos(4t)[u(t +4) – ut - 4)] Using only the Fourier the transform table and properties
3. (5 points) Find the solution u(x,t) of the equation ut = uxx, subject to the boundary conditions u(0,t) = 1, u(2,t) = 3, and the initial condition u(x,0) = 3x + 1.
Find all of the solutions to the equation cos(t) = a) t = 4 + ka or t= 7* + ka, kez b) t = 8 + 2kr or t = 7* + 2ka, ke Z c) t = 8 + ka or t = 3* + ka, kez d) t = 1 + 2kr or t = 3 + 2ka, ke Z e) t = 31 + 2kt or t = 5x + 2ka, kez
An hourglass sand timer drips 2 cm^3 of sand every minute. It has a radius of 4cm and a height of 15cm. When there is 7cm of sand in the hourglass, what rate is the depth of the sand decreasing (dv/dt) AND what is the rate that the radius is changing (dr/dt)? (This is a cone problem) HOW I NEED IT SET UP: EXAMPLE BUT WITH CYLINDER LENGTH AND RADIUS: v(t)= π ((r(t)^2)’ l(t) + r(t)^2 * l’(t)) product rule:...
(1 point) Solve the nonhomogeneous heat problem Ut Uzz + 3 sin(3.c), 0<x<1, u(0,t) = 0, u(T,t) = 0 u(2,0) sin(52) u(x, t) = Steady State Solution lim oo u(a,t) =
The three blocks have weights of WA = 60 lb, WB = 40 lb, and WC = 20 lb. If the coefficients of static friction at the surfaces of contact are UAB = 0.4, UBC = 0.3, and UCD = 0.2, determine (a) the smallest horizontal force P needed to move block C, and (b) the tension in the cable. Cable attached to the wall and block A a.) P= b.) T = A B Р С D
Problem 4: Consider the following problem for the heat equation (1) (2) (3) ut= Uxa + s(t), xE (0,1), t > 0 u(0, t) 2, u(1, t) = 4 и (х, 0) — 2(1 — х). where s(t) describes the source term (a) Find a series solution for u(x, t) with s(t) = e"1. (b) What is the convergence criteria for the transient extension function if s(t) = 0. Problem 4: Consider the following problem for the heat equation (1)...
Problem 4: Consider the following problem for the heat equation (1) (2) (3) ut= Uxa + s(t), xE (0,1), t > 0 u(0, t) 2, u(1, t) = 4 и (х, 0) — 2(1 — х). where s(t) describes the source term (a) Find a series solution for u(x, t) with s(t) = e"1. (b) What is the convergence criteria for the transient extension function if s(t) = 0. Problem 4: Consider the following problem for the heat equation (1)...