3. Solve the one-dimensional wave equation subject to the following conditions: [v(0,1)= 0, v(7,t)= 0 Lv(x,0)=0, = sin x |t=0
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- Show that the function Z = sin(wct)sin(wx) satisfies the wave equationThe 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 .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. Find
- 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/4A particle's position vector is given by: F(t) = R(1+ cos(wot + q cos wot))& + R sin(wnt + q cos wot)ŷ (= What is the particle's maximum speed? If it helps, you can assume that R, wo, and q are all positive numbers, and that q is very small.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) =
- 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.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) =5C. Under suitable assumptions derive one dimensional wave equation.
- Suppose that a particle follows the path r(t) = 2 sin(3t) i+4 cos(3t) j. Give an equation (in the form of a formula involving x and y set equal to 0) whose whose solutions consist of the path of the particle. = 0. (Answer in terms of x and y.) Determine the velocity vector of the particle when t = T : v(7) = (Answer in terms of t.) Determine the acceleration vector of the particle whent = t : a(7) = (Answer in terms of t.)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) =The motion of a point on the circumference of a rolling wheel of radius 4 feet is described by the vector function r(t) = 4(12t - sin(12t))i + 4(1 − cos(12t))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) = =