4. (10 points) A damped wave train is expressed by f(t) = Ae-iwot when t2t> 0;...
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.
Find the Laplace transform of the function f(t). f(t) = sint if 0 St< $41; f(t) = 0 ift> 41 Click the icon to view a short table of Laplace transforms. F(s)=
2. Solve for the motion of a driven-damped harmonic oscillator whose forcing function F(t) is given by F(t) = 0, < 0 HU t 12 0 <t<T PO) – 4(), 0<t<7 F(t) = A, t>t. m т.
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
Find the Laplace transform of f(0) = 1, for 0 <t<1 5, for 1<t<2. e-l for t > 2
10. Let Ae-at if t > 0 h(t) = 10 ift < 0 where A and a are parameters as in Example 2.21. Show that Α h(x) = (Ch)(i) = Tarla+id)
PLEASE SOLVE BOTH QUESTIONS. THANK YOU!
Find the Laplace transform, F(s) of the function f(t) = t. t > 0 F(s) = ,s > 0 Question Help: Video Message instructor Submit Question Find the inverse Laplace transform of F 88 – 13 $2 – 55 – 6 3 s +1 S - 6 f(t) = Question Help: Message instructor Submit Question
What is the value of i(t) for t>=0? Given L = 10 H, R = 5 ohms and Vs = 40V. URO - w vs 40e^(-0.5t) 20e^(-0.5t) 40e^(-0.02t) 8e^(-0.5t)
please show all steps
Find L{f}(s) directly by evaluating the integral if 2t when 0 <t<3, when t > 3.
5. Given y,-t is a solution of t2y" + 2t1-2y = 0, for t > 0, find a second solution y2.