Question 2. Let (1 H(x) = x > 0 (0 r<0° Solve the wave equation utt Urr = 0 with the following initial valucs: | (а) и(х,0) — Н(»), и (х,0) — 0. (b) u(x,0) = 0, ut(x, 0) = H(x).
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Solved in 3 steps
- 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))A bee with a velocity vector r' (t) starts out at (7, -3, 7) at t = 0 and flies around for 6 seconds. Where is the bee located at time t = 6 if [°r' (Use symbolic notation and fractions where needed.) r' (u) du = 0 location:A particle started at A(1,0) circled the origin once an d returned toA(1,0) .what were the change in its coordinates
- 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 positionWhich of the following is the equation of tangent line of the curve that is given by parametric equations x=e4, y = 2cost+6sin t at the point (1,2) ? ,2t X+5 y == 3 (a) X+11 y = - 6. (b) (c) y = 3x – 1 (d) y= 4x – 2 (е) у%3Dбх — 43. Triangle DEF with vertices D(0, 6). E(3, 5). and F(1, 1): 90° counterclockwise about the point (5, 2) D' L E' (L F'(L
- Show that the function Z = sin(wct)sin(wx) satisfies the wave equationWhich of the following is most suitable solution for wave equation = c2? %3D at2 ax2 .(a) y = (AeP* + Be-P*)(Ce pt + De ept) (b) y = (Acos px + Bsin px)(Ccos cpt + Dsin cpt) (c) y = (Ax + B)(Ct + D) (d) y = (Aepx + Be-px)(Cep*t + De-ep*r) O a O b O c O dThe motion of a point on the circumference of a rolling wheel of radius 3 feet is described by the vector function 7(t) = 3(10t – sin(10t))ỉ + 3(1 – cos(104))} Find the velocity vector of the point. v(t) = Find the acceleration vector of the point. a(t) Find the speed of the point. s(t) =