Solve the following wave equation on the interval [0,T] Utt - c²Uxx = 0, x = [0, π] U(0,t) = 0, U(x,t) = 0 U(x, 0) = 0, Ut(x, 0) = = -12c. cos(x).
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Wave equation interval question. PLEASE DONT GIVE AI GENERATED RESPONSE they always lead me to the wrong answer
![Solve the following wave equation on the interval [0,T]
Utt - c²Uxx = 0, x = [0, π]
U(0,t) = 0, U(x,t) =
0
U(x, 0) = 0, Ut(x, 0) = = -12c. cos(x).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff2437b9d-e2ad-49ef-bf1e-5f1a1e22adaa%2F680f89e7-13cf-46cd-99ae-f62358c6d174%2Fqfw16ab_processed.jpeg&w=3840&q=75)
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- A 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?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.Find 4 dx J-cos(3пx) (ез + 1)dtr.
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- Determine whether the functions fi(x) = cos 3r, f2(x) = x, and f3(r) = cos² r are linearly independent on the interval (-x, 0).2. 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 positionSketch the curve with the vector equation r(t) = cos(t)i − cos(t)j + sin(t)k. Show the direction of increasing t with an arrow drawn on your curve.