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)
- Find the possible values of a and b in the expression u(x, t) = cos (at) sin (bx) such that it satisfies the wave equation.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 feedbackSelect the wave equation by utilizing separate variables with initial conditions?
- Compute the derivatives of the given functions. b) [12 cos¯¹2x] d dx c) d) e) f) 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- FIDetermine 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 position