Using the standard conditions for the wave equation with the boundary conditions listed below to find U(x,t). Uxx = 16Utt U(0,t)=0 U(π,t) = 0 U(x,0)= 0 Ut(x, O) = 2sin(3x).
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- 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 the function Z = sin(wct)sin(wx) satisfies the wave equation6. 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. Find
- The 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(#) =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) =Which of the following are parametric equations for the entire line y = x + 1? Choose all that apply. x(t) = cos(t), y(t) = cos(t) + 1 Ox(t)=t+2, y(t) = t + 3 x(t)=t, y(t) = t + 1 Ox(t)=t+1, y(t) = t Ox(t) = t1, y(t) = t x(t) =tan(t), y(t) = tan(t) + 1 x(t) = t², y(t) = ² + 1 Ox(t) = t³, y(t) = t³ + 1
- Compute the directional derivative in the direction of v at the given point. f(x, y) = e*y-y°, (12, –5), P = (4,4) V = Remember to use a unit vector in your directional derivative computation. (Give an exact answer. Use symbolic notation and fractions where needed.) Du f(4, 4) =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) =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).
- The position vector r describes the path of an object moving in the xy-plane. Position Vector Point r(t) = 4 cos ti + 4 sin tj (V5, 2V5) (a) Find the velocity vector v(t), speed s(t), and acceleration vector a(t) of the object. v(t) = -4 sin(t)i + 4 cos (2)j s(t) 4. -cos(1)i – 4 sin(r) a(t) = COS (b) Evaluate the velocity vector and acceleration vector of the object at the given point. -2V2 i+ 2V2jFind 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+ WThe position vector r describes the path of an object moving in the xy-plane. Position Vector Point r(t) = 6 cos ti + 6 sin tj (3V2, 3V2) (a) Find the velocity vector v(t), speed s(t), and acceleration vector a(t) of the object. v(t) = s(t) a(t) (b) Evaluate the velocity vector and acceleration vector of the object at the given point. E) - =