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...
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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).
)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...
9. Solve the wave equation subject to the boundary and initial conditions u(0,t) = 0, u(x,0) = 0, U(TT, t) = 0, t> 0 $ (3,0) = sin(x), 0<x<a
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...
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 expression of the function u(, 0.5) that represents the spatial profle of the string at timet 0.5. Provide the graph of this function
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...
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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
Consider the inlínitm ar ls sby subject to the initial conditions u(x,0)-f() and u(,0)-9(x) where 0, otherwise (a) What is the wave speed? c (b) What is the domain of dependence for the point (r, t) (2,3)? (c) Using only characteristic lines and your knowledge of d'Alembert's solution, find the following values of u(r,t) c) u9,9)- (b) u2,5)
Consider the inlínitm ar ls sby subject to the initial conditions u(x,0)-f() and u(,0)-9(x) where 0, otherwise (a) What is the wave...
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...
3. Solve the wave equation subject to the conditions u(0,t)=0, u(z,t) = 0 at 2 2 u(x, 0) = 4 =0 at 2 =1
3. Solve the wave equation subject to the conditions u(0,t)=0, u(z,t) = 0 at 2 2 u(x, 0) = 4 =0 at 2 =1
d1=8
d2=9
lu for Find the solution u(x,t) for the l-D wave equation-=- Qx2 25 at2 (a) oo < x < oo with initial conditions u(x,0)-A(x) , where A(x) Is presented in the diagram below, and zero initial velocity. For full marks u(x,t) needs to be expressed as an equation involving x and t, somewhat similar to f(x) on page 85 of the Notes Part 2. d2+5 di+10 di+15dı+20 (b) Check for the wave equation in (a) that if (x...