Question 5: Solve the wave equation initial boundary problem by the method of separation of variables PDE : 81 uxx = Utt, t > 0, 0 < x < 7, ICs: u(0, г) 3 0, и, (0, х) — 4(7 — х), 0<т<7, BCs : u(t, 0) = 0, u(t,7) = 0, | t > 0.
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Q: Question 5: Solve the wave equation initial boundary problem by the method of separation of…
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Q: Question 5: Solve the wave equation initial boundary problem by the nethod of separation of…
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- Which of the following is most suitable solution for wave equation = c2? %3D at2 ax2 .(a) y = (AeP* + Be-P*)(Ce pt + De ept) (b) y = (Acos px + Bsin px)(Ccos cpt + Dsin cpt) (c) y = (Ax + B)(Ct + D) (d) y = (Aepx + Be-px)(Cep*t + De-ep*r) O a O b O c O dfor wave equation, seperation of vairables u(x,t)=X=(x)T(t)= Use variables separation method to solve the wave equation uxxutt. This function is defined on spatial domain 0 0. Subject to boundary conditions: ux(0, t) = u,(a, t) = 0 and initial conditions: u(x, 0) = 0 and u₁(x,0) = f(x)
- 5C. Under suitable assumptions derive one dimensional wave equation.) Solve the inhomogeneous wave equation on the real lineUtt − c2Uxx = sin x, x ∈ RU(x, 0) = 0, Ut(x, 0) = 0.Explain what theory you are using and show your full computations.a2u satisfies the wave equation əx² -n a²u Verify that U(x, t) = e¬Vkt cos\ax %3D k at2
- 3. Solve the radial wave in R3 with initral data gler) =4-r², Yer)=0 equation = Au U, =Which of the following are parametric equations for the elllpse glven by +y'%3D17 Choose all that apply. Oz(t) = - 3 cos(t), y(t) = - sin(t) Oz(t) = 3 cos(t - 7), y(t) = sin(t– w) Oz(t) = 3 cos(5t), y(t) = sin(5t) O z(t) = cos(t), y(t) = sin(t) Dz(t) = cos(t), y(t) = 3 cos(t) O z(t) = 3 sin(t), y(t) = cos(t) O (t) = 9 cos(t), y(t) = sin(t) Or(t) = 3 cos(t), y(t) = sin(t)Please short steps and final answer. Solve the wave equation using Fourier Transform: o'u ou - c0 0 %3D -12x utx, 0) = H(x)e %3D u,(x, 0) = 0. Oa. u (x, t) = Real sin wt (12+iw) %3D 2 я Ob. 1 iwx u (x,t) Real cos wt dw (12+iw) Oc. iwx u (x,1) Real sın wt %3D w (12+iw) Od. 1 u (x,1) = Real cos wt w (12+iw) Oe correct ancue
- Q2) Solve the wave equation u=u 00 " XX 11 subject to u(0,t) = u(2,t) =0, t>0 and u(x,0)=0, u )=0, u,(x,0): = sin (3лx), 0The parametric equation of the x_axis is t=1 O x=1 O x=0 O x=t2. The position vector of a particle is given by r(t)= (2 cos t sin t)i +(cos^2 t - sin^2 t)j + (3t)k If the particle begins its motion at t = 0 and ends at t = pi, find the difference between the length of the path traveled and the distance between start position and end positionSEE MORE QUESTIONS