1. Solve the vibrating string problem PDE BC BC IC IC utt T.T Uz(0,t) = 0...
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
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
5. For the transport equation PDE Uz-ut + u = 0 IC u(z,0) cos z (a) What is the associated ODE after applying the method of characteristics? (b) Solve the associated ODE to find u(s,T) c)Find u(x, t) 5. For the transport equation PDE Uz-ut + u = 0 IC u(z,0) cos z (a) What is the associated ODE after applying the method of characteristics? (b) Solve the associated ODE to find u(s,T) c)Find u(x, t)
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 answer question number 2, Thank you Engineering Mathematics (-) # 6 HM. olve the PDE of the vibrating string with given initial velocity and zero initial displacement by use of Fourier sine series. 02u(x,t) = c2-211(x,t) ax2 PDE. : t>0 0<x<L 2 , Ot , BCs u(0,1) 0u(L,t) 0, t20 IC u(x,0) = 0 , 0 x L : an(x,0) =h(x) 0 L x , ot in problem (1), u(x,t)=? (2). Suppose that h(x)-x(1-cos(-)) Engineering Mathematics (-) # 6...
3. (20 pts). Find the solution to the vibrating-string problem: utt u(0,t) u(L,t) u2,0) 2,0) = 0 = 0 2 sin(27/L) + sin(31/L) sin(72/L) 0<<L, 0<t< 0<t< oo 0<t< 0<r<L 0<r<L
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)...
Assignment 0220 Marks) Solve the following IVBP: PDE : Uxx = (1/25) utt ICs: u (x,0) = x2 (nt - x), ut (x,0) = sin(x) BCs: u(0,t) = 0, u(nt,t) = 0 for 0<x<, t> 0. for 0<x<T. for t>0.
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...
9. Consider the beam PDE for the transverse deflection u(x, t) of an elastic beam Utt + Kurz = 0 for 0 < x <L (30) where K > 0 is a constant. Suppose the boundary conditions are given by (31) u(0, t) = uz(0,t) = 0 Uwx (L, t) = Uzzz(L, t) = 0 (32) and the initial conditions are (33) u(x,0) = (x) u1(x,0) = V(x) (34) Use separation of variables to find the general solution to the...