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7. Solve the vibrating membrane problem (symmetric case) 11(a,t) = 0 u(r,0) = f(r) u,(r, 0) = g(r...
9. Solve the vibrating membrane problem 11(r,θ,0) = f(r,0) b) F(r, θ) = 0. g(r, θ) = (1-rrsi20, a...
9. Solve the vibrating membrane problem 11(r,θ,0) = f(r,0) b) F(r, θ) = 0. g(r, θ) = (1-rrsi20, a = c = 1.
9. Solve the vibrating membrane problem 11(r,θ,0) = f(r,0) b) F(r, θ) = 0. g(r, θ) = (1-rrsi20, a = c = 1.
Solve the circularly symmetric vibrating membrane PDE given as u_tt = ∇^2*u BC : u(1, θ,...
Solve the circularly symmetric vibrating membrane PDE given
as
u_tt = ∇^2*u
BC : u(1, θ, 0) = 0, 0 < t < ∞
ICs :
u(r, θ, 0) = J_0*(2.4r) − 0.25*J_0*(14.93r), 0 ≤ r ≤ 1
u_t(r, θ, 0) = 0
Solve the circularly symmetric vibrating membrane PDE given as Utt = Dau BC : u(1,0,0) = 0, 0<t< oo ICs : u(r,0,0) = J.(2.4r) – 0.25J(14.93r), 0 <r <1 Ut(r,0,0) = 0
Solve the Dirichlet problem in an infinite strip uxx + uyy=0 for x ϵ R and 0 <y <b , u(x,0)=f(x) , u(x,b)=g(x). (...
Solve the Dirichlet problem in an infinite strip
uxx + uyy=0
for x ϵ R and 0 <y <b ,
u(x,0)=f(x) ,
u(x,b)=g(x). (Hint: first
do the case f=0. The case g=0 reduces to this one
by the substitution y→ b-y , and the case general is
obtained by superposition)
4. Solve the Dirichlet problem in an infinite strip: uxx + Uyy 0 <у<b, u(x, 0) — S(x), и(х, b) — g(x). (Hint: First do the case The case g...
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 solu...
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...
11. Solve this boundary value problem for u(x, t): n2 xu,-(x14),--11 (0
11. Solve this boundary value problem for u(x, t): n2 xu,-(x14),--11 (0<x <c,0 11 (c, 1) = 0, u(x, 0) = f(x), where u is continuous for0sxc,0 and where n is a positive integer. Answer: u(x, 1) Σ A,Jn(gjx) exp (-α,1), where a", and A, are the constants j-1
11. Solve this boundary value problem for u(x, t): n2 xu,-(x14),--11 (0
1- Consider waves propagating in a vibrating quarter-circular membrane: at2 The displacement u(r,...
1- Consider waves propagating in a vibrating quarter-circular membrane: at2 The displacement u(r, e t) is zero on the entire boundary at all times. a) Write down explicitly the three boundary conditions expressed above. b) Starting by the method of separation of variables, find the solution and show that it is given by ui (r, θ' t) = Σι Σ J1(A ct) sinde) [A, cos(JA Ct)+B, sin(vA ct)], where l is a positive even integer, and n is a positive...
Problem 2.7.26. Solve the parabolic problem ubject to the nonhomogeneous boundary conditions u(t,0)-1 and u(t,1)or 0 and the initial condition u(0,x)(x for xE(0,1) for some given function f:(0,1) R....
Problem 2.7.26. Solve the parabolic problem ubject to the nonhomogeneous boundary conditions u(t,0)-1 and u(t,1)or 0 and the initial condition u(0,x)(x for xE(0,1) for some given function f:(0,1) R.
Problem 2.7.26. Solve the parabolic problem ubject to the nonhomogeneous boundary conditions u(t,0)-1 and u(t,1)or 0 and the initial condition u(0,x)(x for xE(0,1) for some given function f:(0,1) R.
please solve B? and C) The total energy for the vibrating string problem can be written...
please
solve B? and C)
The total energy for the vibrating string problem can be written as E = Kinetic Energy + Potential Energy = dx. Consider the case where u(r, t) satisfies the wave equation with the boundary con ditions ux(0,t) 4(L, t)-0. (a) Show that E is constant in time (b) Calculate the energy in 1 mode. (c) Show that the total energy is the sum of the energies contained in each mode
The vibrating string problem is given by the equations below. Solve this problem with α-2L and th...
The vibrating string problem is given by the equations below. Solve this problem with α-2L and the initial functions f(x-7 sin 8x + 19 si 10x and a x-0. Ul 0<x<L,t0 t2 0 t2 0 ot u(x,0) f(x) 0sxSL du u(L,t) = 0 u(x,t) = X Sorry, that's not correct. Sorry, your answer is not correct. Correct answer: 4 cos (21t) sin (7x)+17 cos (30t) sin (10x) Your answer a Similar Question Next Question
The vibrating string problem is given...
Need help with this problem. BC 1. Solve the vibrating string problem PDE Uz = 4uzz...
Need help with this problem.
BC 1. Solve the vibrating string problem PDE Uz = 4uzz uz(0,t) = 0 ВС uz(1,t) = 0 IC u(a,0) = cos(372) (3,0) = r 0<x< 1, 0 <t< oo 0<t< 0<t<oo 0<x<1 0<x<1. IC
9. Solve the vibrating membrane problem 11(r,θ,0) = f(r,0) b) F(r, θ) = 0. g(r, θ) = (1-rrsi20, a = c = 1.
9. Solve the vibrating membrane problem 11(r,θ,0) = f(r,0) b) F(r, θ) = 0. g(r, θ) = (1-rrsi20, a = c = 1.
Solve the circularly symmetric vibrating membrane PDE given
as
u_tt = ∇^2*u
BC : u(1, θ, 0) = 0, 0 < t < ∞
ICs :
u(r, θ, 0) = J_0*(2.4r) − 0.25*J_0*(14.93r), 0 ≤ r ≤ 1
u_t(r, θ, 0) = 0
Solve the circularly symmetric vibrating membrane PDE given as Utt = Dau BC : u(1,0,0) = 0, 0<t< oo ICs : u(r,0,0) = J.(2.4r) – 0.25J(14.93r), 0 <r <1 Ut(r,0,0) = 0
Solve the Dirichlet problem in an infinite strip
uxx + uyy=0
for x ϵ R and 0 <y <b ,
u(x,0)=f(x) ,
u(x,b)=g(x). (Hint: first
do the case f=0. The case g=0 reduces to this one
by the substitution y→ b-y , and the case general is
obtained by superposition)
4. Solve the Dirichlet problem in an infinite strip: uxx + Uyy 0 <у<b, u(x, 0) — S(x), и(х, b) — g(x). (Hint: First do the case The case g...
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...
11. Solve this boundary value problem for u(x, t): n2 xu,-(x14),--11 (0<x <c,0 11 (c, 1) = 0, u(x, 0) = f(x), where u is continuous for0sxc,0 and where n is a positive integer. Answer: u(x, 1) Σ A,Jn(gjx) exp (-α,1), where a", and A, are the constants j-1
11. Solve this boundary value problem for u(x, t): n2 xu,-(x14),--11 (0
1- Consider waves propagating in a vibrating quarter-circular membrane: at2 The displacement u(r, e t) is zero on the entire boundary at all times. a) Write down explicitly the three boundary conditions expressed above. b) Starting by the method of separation of variables, find the solution and show that it is given by ui (r, θ' t) = Σι Σ J1(A ct) sinde) [A, cos(JA Ct)+B, sin(vA ct)], where l is a positive even integer, and n is a positive...
Problem 2.7.26. Solve the parabolic problem ubject to the nonhomogeneous boundary conditions u(t,0)-1 and u(t,1)or 0 and the initial condition u(0,x)(x for xE(0,1) for some given function f:(0,1) R.
Problem 2.7.26. Solve the parabolic problem ubject to the nonhomogeneous boundary conditions u(t,0)-1 and u(t,1)or 0 and the initial condition u(0,x)(x for xE(0,1) for some given function f:(0,1) R.
please
solve B? and C)
The total energy for the vibrating string problem can be written as E = Kinetic Energy + Potential Energy = dx. Consider the case where u(r, t) satisfies the wave equation with the boundary con ditions ux(0,t) 4(L, t)-0. (a) Show that E is constant in time (b) Calculate the energy in 1 mode. (c) Show that the total energy is the sum of the energies contained in each mode
The vibrating string problem is given by the equations below. Solve this problem with α-2L and the initial functions f(x-7 sin 8x + 19 si 10x and a x-0. Ul 0<x<L,t0 t2 0 t2 0 ot u(x,0) f(x) 0sxSL du u(L,t) = 0 u(x,t) = X Sorry, that's not correct. Sorry, your answer is not correct. Correct answer: 4 cos (21t) sin (7x)+17 cos (30t) sin (10x) Your answer a Similar Question Next Question
The vibrating string problem is given...
Need help with this problem.
BC 1. Solve the vibrating string problem PDE Uz = 4uzz uz(0,t) = 0 ВС uz(1,t) = 0 IC u(a,0) = cos(372) (3,0) = r 0<x< 1, 0 <t< oo 0<t< 0<t<oo 0<x<1 0<x<1. IC
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