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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- Show that the function Z = sin(wct)sin(wx) satisfies the wave equationLet f(x,t)=cos(12x+4t). Find the value of K so that f satisfies the wave equation ∂^2f/∂x2=K∂^2f/∂t^2Solve 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 .Show that cos(ωt − β), cos ωt, sin ωt are linearly dependent functions of t.find the acceleration of a particle whose position function is x(t)=sin(2t)+cos(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) =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.Show that the function z = cos(4x + 4ct) satisfies the wave equation ∂2 z/ ∂t2 = c2 (∂2 z /∂x2 ).
- What did you write for the wave equation at the beginning? is that the same as Schrodinger's Eq.?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) =Eliminate the parameter t from the parametric equationsx =3 +sin t and y = cos t - 2.