a2u satisfies the wave equation əx² -n ə?u Verify that U(x, t) = e¬Vkt cos\TX k at2
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A: Solution
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- 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) =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.The graph of f (θ) = Acos θ + B sin θ is a sinusoidal wave for any constants A and B. Confirm this for (A,B) = (1, 1), (1, 2), and (3, 4) by plotting f .
- find the acceleration of a particle whose position function is x(t)=sin(2t)+cos(t)The graph of f(0) = A cos 0 + B sin0 is a sinusoidal wave for any constants A and B. Confirm this for (A, B) = (1, 1), (1, 2), and (3, 4) by plotting f.If r(t) = cos(lt)i + sin(lt)j - 4tk, compute the tangential and normal components of the acceleration vector. Tangential component aÃ(t) = ¯ Normal component an(t) =