QUESTION 8 Find the convolution product 2* cos(2t)=
Find the solution of the ordinary differential equation + ky = -2t cos 2t, d+2 dt subject to the initial conditions y(0) = y'(0) = 0, where k is a constant, with k > 4, k + 8.
Solution steps plz
3. Derive the convolution product e" * cos bt by using the formula for the Laplace transform of the convolution.
all parts
-2t e - (13 points) Let f(t) cos 2t, sin 2t) for t 2 0. F() (a) (4 points) Find the unit tangent vector for the curve d (F(t)-v(t)) using the product rule for dt (b) (5 points) Let v(t) = 7'(t). Calculate the dot product and simplify v(t) (c) (4 points) For an arbitrary vector-valued function 7 (t) with velocity vector = 1, what can be said about the relationship between F(t) and v(t)? if F(t) (t)...
Using the convolution property of Fourier Transform to find the following convolution: sinc (t) * sinc (4t): [Hint: sinc (t) ön rect(w/2)] sinc(t)sinc(2t) 8 TT 2 sinc(t) п sinc (2t) п sinc (4t) 4
If u(t) = sin(2t), cos(2t), t and v(t) = t, cos(2t), sin(2t) , use Formula 5 of this theorem to find d dt u(t) × v(t) .
Questions 9-11 all deal with the same curve: Consider the curver(t) = (cos(2t), t, sin(2t)) Find the length of the curve from the point wheret = 0 to the point where t = 71 O 75.7 G O 7/3.7 2. O 7V2.7 2 7.T 2 3 (Recall questions 9-11 all ask about the same curve) Find the arc-length parametrization of the curver(t) = (cos(26), t, sin(2t)), measure fromt O in the direction increasing t. Or(s) = (cos(V28), V28, sin(28)) Or(s)...
QUESTION 6 Find 2 45 s2 + 25-3 5 (write 5/6 by and sin(2t) or cos(31) by sin(2t) or cos(3t). 6.ey-3t) by e-3t 5 points
Use the given information to find each value. cost = 0<t<A/2 (a) cos 2t (No Response) (b) sin 2 (No Response) (c) cos(1) (No Response) (d) sin() (No Response) 28. - 2 POINTS FDPRECALC5 4.9.005. MY NOTES ASK YOUR TEACHER Let the angles of a triangle be a, b, and y, with opposite sides of length a, b, and c, respectively. Use the Law of Sines to find the remaining sides. (Round your answers to one decimal place.) a =...
Find the convolution product 3e-t*e2t-