Please just explain parts d and f. Part d is 0 and f is true
do question 3 with the info provided f 0 Question 3 Given the graph above represents a string being plucked at point (g). The wave equation generated when the string is released after being plucked, is given by the wave equation in question 1, and that additionally: 1. u(0, t) 0 u(4, t) 2. u(x, 0) f(x) as in question 2 au 3. atlt-0 Solve wave equation subject to the restrictions above. [10] Question 2 a) In the General Fourier...
6.[10] Find the solution to the vibrating string problem governed by the given initial-boundary value problem: 9uxx = Utt 0<x< 1, t> 0 u(0,t) = 0) = u(tt,t), t> 0 u(x,0) = sin 4x + 7 sin 5x, 0<x< 1 uz (3,0) = { X, 0 < x < 1/2 r/2 < x <
Please detail Please detail PDE Utt = Uzx + 2a sin(at) sin(1x) 0 < x <1 0<t< oo BCS S u(0,t) = 0 | u(1,t) = 0 0<t< oo ICs u(x,0) = 0 | u4(,0) = sin(nx) 0 < x <1 u (0,t) = f (t) u (L,t) = g(t) S Use sine transform Uz (0,t) = f(t) uz (L,t) = g(t)) Use cosine transform 2 L S [u (x,t)] = Sn (t) = 1 | u(x, t) sin (ntx/L)...
Mark which statements below are true, using the following Consider the diffusion problem u(0,t)=0, u(L,t)=50 where FER is a constant, forcing term Any attempt to solve this using separation of variables fails. This is because the PDE is not homogeneous. A more fruitful approach arises from splitting the solution into the sum of two u(z,t) = X(z)T(t) + us(z), where the subscript designates the function as the steady limit and does not represent a derlvative. BEWARE: MARKING A STATEMENT TRUE...
nonhomogeneous vibrating string problem for u(x with homogeneous boundary conditions t > 0 u(0, t) u(r,t) = 0, 0, = and the initial conditions 0stst tr(z,0)=0, u(z, 0) sin(2x), = Find the solution u(x,t) to the IBVP using an eigenfunction expansion: u(z, t) = Σ an(t) sin(nz) n-1 nonhomogeneous vibrating string problem for u(x with homogeneous boundary conditions t > 0 u(0, t) u(r,t) = 0, 0, = and the initial conditions 0stst tr(z,0)=0, u(z, 0) sin(2x), = Find the...
Please do all four parts for positive feedback. Solve the boundary-value problem for a string of unit length, subject to the given conditions. u(0,t) = 0, u(1,t) = 0, u(x, 0) = f(x), ut(x, 0) = g(x) f(x) = 1/20 sin πx, g(x) = 0, α = 1/π u(0,t) = 0, u(1,t) = 0, u(x, 0) = f(x), ut(x, 0) = g(x) f(x) = sin πx cos πx, g(x) = 0, α = 1/π u(0,t) = 0, u(1,t) = 0,...
parts a,b, c Problem 1. Consider the vibration of a string with two ends fixed. In addition, assume that the string is initially at rest. The initial boundary value problem (IBVP) is written as u(0,t) -u(1,t) u(x,0) = f(x), 0 ut (z, 0-0, 0 < x < 1. The solution of this IBVP using the method of separation of variables is given by n-l a) Find the coefficients bn. b) Show that this wave function can be written as the...
3. In the problems below, you may use the formal solution of the appropriate partial differential equation and boundary conditions from course notes and the text. You do not have to derive the formal solution. (a) (15 points) Find the solution of the initial-boundary value problem du du ət – Ər2 t> 0, 0 < x <7, u(0,t) = , t>0, u( ,t) = 0, t>0, u(x,0) = sin 2x, 0<x< 7. (b) (10 points) Solve the initial-boundary value problem...
I want just c^n Let u be the solution to the initial boundary value problem for the Heat Equation, дли(t, х) — 5 дғи(t, х), te (0, co) хE (0, 1); with initial condition хе х, u(0, х) %—D f(x) 1 хе 2 and with boundary conditions u(t, 0) 0 дди(t, 1) 3 0. Find the solution u using the expansion u(t, х) = "(х)"n ()"а ", n=1 with the normalization conditions | Un(0) 1 Wn = ]. (2n -...
3. [4] The solution of the wave equation02, which satisfies the boundary conditions u(0,t) = u(2,t) 0, is given by a cos+b sin If u(, t) satisfies the initial conditions u(x, 0)-0 and u(x,0)3sin(Tx) - sin(3T), find the coefficients an and bn Solution: b2 = , bs =- π 97T bn-0 otherwise, and an - 0 for all n 21. 3. [4] The solution of the wave equation02, which satisfies the boundary conditions u(0,t) = u(2,t) 0, is given by...