Obtain the solution of the wave equation u 12 under the following conditions (i) u(0, t) = u(2, t) = 0 (ii) u(x, 0) sin (Tx/2) (iii) ut(x, 0) = 0 using the separation of variables. %3D %3D
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- ii. Find parametric equations for the Line through (7, 5) and (-5, 7) 7. Calculate dy/dx at the point indicated: f(0) = (7tan 0, cos O), 0=a/4Generate a 3D plot based on the equation z=sin(x) +cos(y), both x and y range from 0 to 2 pi. Please use Matlab to solve.Find the position vector for a particle with acceleration, initial velocity, and initial position given below. ä(t) = (5t, 6 sin(t), cos(3t)) 7(0) = (−2, —2, 5) 7(0) = (0, -4,0) F(t) = ( 5³ - 2t 6 > Question Help: Video Submit Question Search -6 sin (1) - 8t - 4 X cos(3t) + 5t+ W
- The motion of a point on the circumference of a rolling wheel of radius 2 feet is described by the vector function r(t) = 2(23t sin (23t))i + 2(1 - cos(23t))j - 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) =1. Find the second derivative of the parametric equations x = a cos t and y = b sin t 2. Use second order derivative to derive the acceleration, a for an object that falls where its movement is described by s = V,t + gt? %3DA baseball is hit at 120 ft/sec from the ground at a 300 angle to the horizontal from a height of 3 feet above home plate. In parametric form we get that the trajectory of the baseball and its location at any time t is given by (x(t), y(t)) where x(t) = 120(cos(30°))· ty(t) = -16t2 + 120(sin(30°)) · t + 3 a. Find dx/dt and dy/dt b. Find the slope of the tangent line to the curve at time t = 2 seconds. c. Show how to find the maximum height of the baseball using parts a and b.
- The wave equation describes the motion of a waveform: 0 u/ôt? – d²u/ðx² = 0. Which of the following functions does not satisfy the wave equation? u(x, t) = sin(x)sin(t) u(x, t) = sin(x – t) + cos(x + t) u(x, t) = sin(x – t) u(x, t) = sin(x – t) + cos(x – t) - None of the functions shown.Find the equation of the tangent line of the parametric equations x = 2 – 3 cos 0, y = 3+ 2 sin 0 at the points (–1,3) and (2,5). .The motion of a point on the circumference of a rolling wheel of radius 5 feet is described by the vector function r(t) = 5(11t sin(11t))i +5(1 − cos(11t))] Find the velocity vector of the point. v(t) Find the acceleration vector of the point. ä(t) = Find the speed of the point. s(t) =
- The motion of a point on the circumference of a rolling wheel of radius 3 feet is described by the vector function 7(t) = 3(13t – sin(13t))ỉ + 3(1 – cos(13t)) 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) =6. Find the position vector 7(t) velocity vector v (t),acceleration a (t), and the speed for the motion of a particle described with parametric equations: a = 3 sin(2t), the distance that the particle travels from t = 0, to t = r. y = 3 cos(2t), z = 2t – 1. FindThe position vector r describes the path of an object moving in the xy-plane. Position Vector Point r(t) = 2 cos ti + 2 sin tj (VZ, V2) (a) Find the velocity vector, speed, and acceleration vector of the object. v(t) = s(t) a(t) = (b) Evaluate the velocity vector and acceleration vector of the object at the given point. a(#) =