Problem 2 (10 points). Consider the wave equation for a vibrating string of infinite length with the initial conditions where the initial displacement f(x) is specified as 0, if 21 Determine the...
)Consider the wave equation for a vibrating string of semi-infnite length with a fixed end at z = 0, t > 0 a(0,t) = 0, and initial conditions 0 < x < oo u(z,0) = 1-cos(nz), ut(x,0) = 0, Complete the table below with the values of u(0.5, t) at the specified time instants 0.5 0.5 x 0.5 0.5 0.5 2 0.5 0.75 t 0.25 u(x,t) )Consider the wave equation for a vibrating string of semi-infnite length with a fixed...
Partial Differential Equation - Wave equation : Vibrating spring Question 2 A plucked string, Figure 2 shows the initial position function f (x) for a stretched string (of length L) that is set in motion by moving t at midpoint x =-aside the distance-bL and releasing it from rest timet- 0. f (x) bL Figure 2 (a) If the length of string is 10cm with amplitude 5cm was set initially, state the initial condition and the boundary conditions for the...
u(x, t) represents the vertical displacement of a string of length L = 16 with wave equation 25uxx = uft at position x along the string and at time t Find u(x, t) if a. the initial velocity of the string is 0 and the rightmost position b. the initial velocity is a constant 5 and the vertical displacement is 0. c. the initial velocity is a constant 5 and the rightmost position is held at a vertical displacement of...
Consider the vibrating string on 0 with an initial wave profile, u(x,0)-() 2(1 -x) and initial velocity u(x, 0) 1. Use the method of reflections to find the value of ( Assullie i.be wave speed ise. %. Consider the vibrating string on 0 with an initial wave profile, u(x,0)-() 2(1 -x) and initial velocity u(x, 0) 1. Use the method of reflections to find the value of ( Assullie i.be wave speed ise. %.
r Extra Credit: Write a complete analysis of the wave equation with friction for a string of length L subject to initial conditions u(x, 0)-f(x) and (x,0) (t) r Extra Credit: Write a complete analysis of the wave equation with friction for a string of length L subject to initial conditions u(x, 0)-f(x) and (x,0) (t)
pls help 3. Solve the wave equation for a string of length π for initial conditions u(z,0-2(x-7), boundary conditions u (0, t)-0 u(n, t). (x,0)-0 and
please show work i will rate you Extra Credit: Write a complete analysis of the wave equation with friction for a string of length L subject to initial conditions u(x,0) = f(x) and 쓿(x,0) = g(t). Extra Credit: Write a complete analysis of the wave equation with friction for a string of length L subject to initial conditions u(x,0) = f(x) and 쓿(x,0) = g(t).
1. Wave equation. Consider the wave equation on the finite interval (0, L) PDE BC where Neumann boundary conditions are specified Physically, with Neumann boundary conditions, u(r, t) could represent the height of a fluid that sloshes between two walls. (a) Find the general Fourier series solution by repeating the derivation from class now considering Neumann instead of Dirichlet boundary conditions. Your final solution should be (b) Consider the following general initial conditions u(x, 0)x) IC IC Derive formulas that...
(a) Consider an elastic string of length 10 whose ends are held fixed. The string is set in motion with no initial velocity from an initial postion J2/4 0<x<8 u(x,0) = { 0 8 << 10 Assuming the string is elastic enough to assume this initial configuration, i. Find the Fourier sine series for f (extended as an odd periodic function of period 20). ii. Assuming the propagation speed a = 2 solve the wave equation to find the displacement...
(The wave equation) Consider a string with fixed zero ends of length L with speed parameter c, with initial position -X u(x,0) = x € (0, L/2] c [L/2, L] C L and zero initial velocity. (a) Find the normal modes of the solution and specify the spatial and temporal frequencies for each. (You do not need to derive the general solution to the wave equation with fixed ends.) (b) Describe how the tension Th, density p and length L...