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- Find the solution of the wave equation when initial velocity equal to 0 and initial deflection is (2kx/l) when x between zero and (1/2) and deflection equal to (2k(l-x)/I) when x between (1/2) and (I) the P.D.E. is * c2 dx²2. 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 positionfor wave equation, seperation of vairables u(x,t)=X=(x)T(t)
- Eliminate the arbitrary constant a from the equation (z - a) + y = a° O = + 2ryy" O = + 2ry' Ov =r+ 2ryy O-r+ 2ry'Show that the function Z = sin(wct)sin(wx) satisfies the wave equationSolve 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.
- find the acceleration of a particle whose position function is x(t)=sin(2t)+cos(t)Find the solution of the wave equation when initial velocity equal to O and initial deflection is (2kx/l) when x between zero and (1/2) and deflection equal to (2k(l- x)/I) when x between (1/2) and (1) the P.D.E. is * dt? dx²A particle is moving with velocity V(t) = ( pi cos (pi t), 3t2+ 1) m/s for 0 ≤ t ≤ 10 seconds. Given that the position of the particle at time t = 2s is r(2) = (3, -2), the position vector of the particle at t is?
- 1/w If h(w) Cos 29 -dx then 10 = (m),4Find r'(t). r(t) : (tan-(6t))i+t cos(t)j – Vtk NOTE: Enter your answer in terms of i, j, and k. r'(t)If r(t) = cos(7t)i + sin(7t)j – 3tk, compute the tangential and normal components of the acceleration vector. COS Tangential component ar(t) Normal component an(t) =