Solve the following wave equation on [−1,1] utt(x,t) = uxx(x,t), u(−1,t) = 0. u(1,t) = 0, u(x,0) = f(x), ut(x,0) = g(x).
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Solve the following wave equation on [−1,1]
utt(x,t) = uxx(x,t),
u(−1,t) = 0.
u(1,t) = 0,
u(x,0) = f(x),
ut(x,0) = g(x).
Step by step
Solved in 5 steps with 5 images
- Show that cos(ωt − β), cos ωt, sin ωt are linearly dependent functions of t.for wave equation, seperation of vairables u(x,t)=X=(x)T(t)Show whether the following functions are wave functions or not. 1. У(х, t) еxp(ikx) = A- exp (i(ot-Ф)) кЗх3-0313-3kоxt(kx-ot)-iф)) 2 У(х, t) 3. y(x, t) Aexp(i(k³x³-w³t³-3kwxt(kx-wt)-ip)) Аехр (i(-kx? + оt))
- how would I find the domain of the vector function r(t)=cos(t)i+ln(t)j+1/(t-4)k?find the acceleration of a particle whose position function is x(t)=sin(2t)+cos(t)Q1:- Find the domain of the following vector functions:- (a) f (t) = (cos t)i – Ln(t)j + vt – 2k (b) f (t) = Ln|t – 1|i + e'j + vtk Q2:- Find the domain and the range of the following equations:- 1 -1 (1)W (2)W = sin x y (3)W x²+y2 ху 1 (4)W (5)W = /x² + y2 + z² (6) W = x – y x²+y2+z² (7)W = Ln(x² + y²) (8) W = xy (9) W = 4x² + 9y²
- 8) Find the position vector r(t) for a particle with acceleration a(t) = (5t, 5 sin t, cos 6t), initial velocity (0) = (3, -3, 1) and initial position (0) = (5, 0, -2).Define two vector functions (t) 9 sin(t)+7 cos(t)] + (t³ - 15) k = = (t) 7 sin(t)+9 cos(t)] + tk = . Compute (t) (t) =Consider the wave equation 0 0, with u(0,1) = 1(xt)= 0, u(x,0) = sin x and =0 at t=0. Then u is
- a2u satisfies the wave equation əx² -n a²u Verify that U(x, t) = e¬Vkt cos\ax %3D k at2Solve 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.Determine whether the functions fi(x) = cos 3r, f2(x) = x, and f3(r) = cos² r are linearly independent on the interval (-x, 0).