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.
5. Given y,-t is a solution of t2y" + 2t1-2y = 0, for t > 0, find a second solution y2.
10 sin 2t if 0 <t< 4. (a) Let r(t) if t > T Show that the Laplace transform of r(t) is L(r) 20(1 - e - e-78) 32 + 4 (b) Find the inverse Laplace transform of each of the following functions: s – 3 S2 + 2s + 2 20 ii. (52 + 4)(52 + 25 + 2) 20e-S ini. (s2 + 4)(52 + 25 + 2) (c) Solve the following initial value problem for a damped mass-spring...
Find the Laplace transform of f(0) = 1, for 0 <t<1 5, for 1<t<2. e-l for t > 2
4. (10 points) A damped wave train is expressed by f(t) = Ae-iwot when t2t> 0; and f(t) = 0 ortherwise. a) Please find the power spectrum of this light; b) Please plot and discuss the spectrum when to = 5
Problem (10 pts) Let a function g(a) be given by the following: cos(ma), 0, 0 < α < 2 else g(a)- Let p(t) 3g2 (4 -0.5t). Plot the p(t) waveform over the time range 0 ts 10.
Find i(t) for t> 0 in the given circuit. Assume v;= 34 V. t=0 10 22 6022 [i(t) 1 mF Vi + 40 Ω 2.5 H O (0) = –10.88te-20+ (0) A i(t) = -27.20 te-20tu(t) A i(t) = 13.60te-20tu() A O i(t) = –17.00 te-20t4() A
1. For the circuit shown below, we wish to find v(t) for t>0. 1 1 a. Find the governing equation for the voltage v using KCL at the top node using the following definitions: a = 0,W, = dr. This will get you a governing equation in the same form as that derived for the case we did in class where the R, L, and C were in series. b. What is the particular solution in this case? c. If...
In the given circuit, identify (0) and i(t) for t> 0. Assume 10) = 0 V and 1(O) = 2.50 A. + 5u(t) A 222 v+0.5 F ell 1 H [3.780 e-t2cos(1.3229t - 90°)]u(1) V [5 + 2.67252 e-t2cos(1.3229t - 200.79] A [0 – 2.67252e-t2cos(1.3229t – 200.7°)] A [5 – 2.67252e-t/2 cos(1.3229t+ 200.79] A [2.673e-t2cos(1.3229t – 90°)]u(0) V [1.336e-t2 cos(1.3229t+ 90°)]/(t) v
value: 10.00 points For the network shown in the given figure, find v(t) for t> 0. Assume L = 0.9 H. 592 692 20 V 2 A 1292 > 200 + v L The voltage v(t) = V for t>0. Hints References eBook & Resources Hint #1 Hint #2 Hint #3 Hint #4 Check my work