P-6 Solve the Wave equation subject to the given condition u(0, t) = 0, u(L, t) = 0, t>0 ди u(x, 0) = 0, = x(Lx), 0
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- 5C. Under suitable assumptions derive one dimensional wave equation.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 dWhat did you write for the wave equation at the beginning? is that the same as Schrodinger's Eq.?
- 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.-5- Question 4 (a) An object is moving with position vector r(t) = cos(cot)i+sin(cot)j + a²k. (i) Determine the velocity and acceleration vector of the object. (ii) If = rads s-¹ and a = 2 m s-² determine the position and velocity of the object at t = 3 s.8) Find the position vector r(t) for a particle with acceleration a(t) = (5t, 5 sin t, cos 6t), initial velocity (0) = (3, -3, 1) and initial position (0) = (5, 0, -2).
- a2u satisfies the wave equation əx² -n a²u Verify that U(x, t) = e¬Vkt cos\ax %3D k at22. 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 positionSolve using wave equation: u(0, t) = u(π, t) = u(x, 0) = 0, du/dt | t = 0 = sin(x)