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Problem 6. (10 pts) Write down the following in the form of x(t) = A cos(2t...
Problem 3 (10 pts) The wavefunction of a particle in an infinite potential well, of width a, is initially given by 16 ?(x, t-0) sin"(? x/a) cos(nx/a) Find the expression for ?(x, t) for all t > 0
Write the parametric equations x=2siny=4cos0 in the given Cartesian form. y^2/16= with x0. Write the parametric equations x=2sin2y=5cos2 in the given Catesian form. y= with 0x2. Write the parametric equations x=4ety=8e−t as a function of x in Cartesian form. y= with x0. Write the parametric equations x = 2 sin 0, y = 4 cos 0, 0<O< in the given Cartesian form. = with x > 0. 16 Write the parametric equations x = 2 sin’e, y = 5 cos?...
+ – for n > 1, subject to Problem 5 (6 pts): Solve the recursive equation T(n the initial condition T(1) = 0.
' cos(3t), t<n/2, 2. Let f(t) = sin(2t), 7/2<t< , Write f(t) in terms of the unit step e3 St. function. Then find c{f(t)}.
252 322 6480 0.25 E 4V /12V Question 11 1 pts 11. The voltage v across the capacitor fort > 0 2exp(-2t) [2cos(2t) - sin(2t)] V 2exp(-t) [2cos(2t) - sin(2t)] V 2exp(-t) (cos(2t) - 2sin(2t)] V 2exp(-t) [2cos(5t) - sin(5t)] V
4. (10 points) Find the solution to the wave problem Ut = c+421 +COSI, <0, t>0, with initial conditions u(1,0) = sin r, 4(1,0) = 1+I.
PROBLEM 4. Determine the function u = u(t, x) if Ut = Uzz, t> 0, x € (0, 7), and u(0, x) = cos (x), uz(t, 0) = uz(t, 7) = 0.
4. Write the initial value problem in matrix form X' = AX + f(t), X (to) =< b1,b2, 63 > and then find the largest interval centered at to =0 where the initial value problem will have an unique solution. '(t) = 3x + 2y - 2+t?, (to) = 3 yt) 2-2y - z+ vt +4, y(to) = 3 z't) 3x + 2y - 2+3, z(to) = 3
Question 11 1p Determine the length of the curve r(t) = (2, 3 sin(2t), 3 cos(2t)) on the interval ( <t<27 47107 Озубл 47 0 250 √107 None of the above or below Previous Ne
Please include step-by-step solution. D19. Solve t2x" +3tx -3 x-t', t>0.