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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- find the acceleration of a particle whose position function is x(t)=sin(2t)+cos(t)Find the direction field for the equation: y' = x + sin(y) + cos (x) at the point A = (0, pi3)Find the value of the derivative dy/dx at t=2π/3 when an object moves according to the parametric equations: x(t) = 2t+sin(2t) and y(t) = 3t−3cos(2t) A) = 3+3√3 / 2-√3 B) = 2 - √3 C) = 3 - 3√3 D) = 1/4 (3 - √3)
- 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.(b) Solve the inhomogeneous wave equation on the real line Utt-c²Uzz = sin x, x ER U(x,0) = 0, Ut(x, 0) = 0. Explain what theory you are using and show your full computations.
- Answer both remaining part in 10 minutes in the order to get positive feedback2. 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 positionConsider (x, y, z) = 4xy²+ 3y sin(z) and at the point P = (1,2,0) calculate the directions in which the function =-4 does not change.
- Compute the derivatives of the given functions. d a) dt c) d b) [12 cos ¹2x] dx d) e) f) [5 sin ¹5t] d. du d dz d dy d = dq [4 sec ¹3u] [10 tan-¹2z -1 [6 csc ¹ 4y] [9 cot-¹39] = = = = = G 4- 9- FIFind the unit tangent vector to the curve defined by F(t) = (5 cos(t), 5 sin(t), 2 sin²(t)) 3T 4 at t= 5 7 (³) = (-2/ T r(t) = y(t) = Use the unit tangent vector to write the parametric equations of a tangent line to the curve at t = 3π 4 5 >(t) =| −1 2 5 √2 2√ 13 Submit Question 5 2v 13 5 2√13 26 t 5 2√13 t X X 26 X X D JUN 13 2 ali SA NThe wave equation describes the motion of a waveform: 0 u/ôt? – d²u/ðx² = 0. Which of the following functions does not satisfy the wave equation? u(x, t) = sin(x)sin(t) u(x, t) = sin(x – t) + cos(x + t) u(x, t) = sin(x – t) u(x, t) = sin(x – t) + cos(x – t) - None of the functions shown.