(2) Solve the following BVP for the Wave Equation using the Fourier Serics solution formulac (42- u(r, t)= 0 u(0, t) 0...
(2) Solve the following BVP for the Wave Equation using the Fourier Series solution formulae. (432 – )u(x, t) = 0 (x, t) € (0,5) x (0,0) (0,t) = 0 t> 0 Zu (5, t) = 0 to u(x,0) = sin(7x) – 12sin(77x) ut(x,0)=0
(3) Solve the following BVP for the Wave Equation using the Fourier Series solution formulac (3a2 u(r, t) 0 u(0, t)0 u(T, t) 0 u(r, 0) sin(x)2sin(4r) 3sin(8r) (r, 0) 10sin(2x)20sin (3r)- 30sin (5r) (r, t) E (0, ) x (0, 0o) t >0 t > 0 1
(3) Solve the following BVP for the Wave Equation using the Fourier Series solution formulac (3a2 u(r, t) 0 u(0, t)0 u(T, t) 0 u(r, 0) sin(x)2sin(4r) 3sin(8r) (r, 0) 10sin(2x)20sin (3r)-...
Solve the BVP for the wave equation (∂^2u)/(∂t^2)(x,t)=(∂^2u)/(∂x^2)(x,t), 0<x<5pi u(0,t)=0, u(5π,t)=0, t>0, u(x,0)=sin(2x), ut(x,0)=4sin(5x), 0<x<5pi. u(x,t)=
(1) Find the solution for each of the following BVP for the heat equation at)u(r, t)0 (r, t) E (0, 20) x (0, co) (0, t) 0 u(20, t)0 u(r, 0) f(r) E [0, 10 E (10, 20 t > 0 1 where f(r) a. t > 0
(1) Find the solution for each of the following BVP for the heat equation at)u(r, t)0 (r, t) E (0, 20) x (0, co) (0, t) 0 u(20, t)0 u(r, 0) f(r)...
Use Fourier transform to solve the following BVP Utt-Uxx=F(x,t) 0<x<1,t>0u(x,0)=f(x)ut(x,0)=0u(0,t)=ux(1,t)=0
Exercise 9. Solve the BVP a(0, t) = 0 u(r, t)-Uz(n, t) = 0 u(z, 0) = sin z 0<x<π, t>0, t >0 t > 0 (z,0) = 0 2
3. Using the linearity of the wave equation, solve the wave equation problem 82u 2 82u a(0, t) = 0 u(L,t)0 u(z,0) = sin( ) (z, 0) = sin( F)
3. Using the linearity of the wave equation, solve the wave equation problem 82u 2 82u a(0, t) = 0 u(L,t)0 u(z,0) = sin( ) (z, 0) = sin( F)
(a) Find the Fourier transform of the following function (b) Using Fourier transforms, solve the wave equation , -∞<x<∞ t>0 and bounded as ∞ f(r)e We were unable to transcribe this imageu(r, 0)e 4(r.0) =0 , t ur. We were unable to transcribe this image f(r)e u(r, 0)e 4(r.0) =0 , t ur.
1 & 5
Solve the following heat equations using Fourier series ux Ut, 0 <x <1,t>0, u (0,t) = 0 = u(1,t), u(x,0) = x/2 1/ 2/ Ux=Ut, 0<x< m ,t>0 ,u(0,t) = 0 = u( 1, t), u(x, O) = sinx- sin3x 3/ usxut, O <x < 1 ,t>0, u(0,t) = 0 = u,(1, t), u(x,0) = 1 -x2 Ux=Ut,O<x <m ,t>0, u(0, t) = 0 = u,( rt , t) , u(x, 0) = (sinxcosx)2 4/ 5/Solve the...
(1) Consider the following BVP for the wave equation, which models a string that is free at both ends: (r, t) E (0, L) x (0, 0o) (0, t) ur(L, t) u(r, 0) f() u(r, 0) g() 0 t0 E [0, L E [0, L The total energy of the solution at time t is 1 E(t) 2 0 (au (r, t) +(u(T, t)? ds. Show that the total energy is constant, i.c., E'(t) 0. [Hint: Start by differentiating under...