4. Find the initial value v(0) and final value v(oo) given: V(s) = s(s+3+28+15) 3s3 +2s+6...
(S3)(s4) The response of the system is given by Y(s) s(s+2)(2s 1) Find the initial value of the system output.
#4 (8 pts.) Consider the following circuit, find (directly from circuit) Find: i(0), v(0), i(oo),v(oo) 4㏀ 12 l㏀ 100mH 100 AF 2 1Q
Consider the initial value problem Let L[y(t)] = Y(3), then Y(s) equals Select one: 2s +2 a. O b. 3s +1 s(232 + s +3) 2s2 + s +1 OC s(2s2 + 8 +3) O d. 2s +1-2/3 252 +8 e. 28 +1 -4/5 28² +8
Let u be the solution to the initial boundary value problem for the Heat Equation au(t,) -48Fu(t,), te (0,oo), z (0,5); with boundary conditions u(t,0) 0, u(t,5) 0, and with initial condition 5 15 15 The solution u of the problem above, with the conventions given in class, has the form with the normalization conditions vn(0)-1, u Find the functions vnwn and the constants cn n(t) wnr) Let u be the solution to the initial boundary value problem for the...
Find a formula for the solution of the initial value problem for for t>0, -oc < x < oo ut = uzz-u a(1:0) = g(z) -x < 1 < x where g is continuous and bounded.( Hint: use v(x, t) = et u(z. t).) Find a formula for the solution of the initial value problem for for t>0, -oc
5] Consider the following initial value problem 9utt = uzz-9r sin(t), (x,0) u(x,0' -oo < x < oo, t > 0, 0, otherwise 0, otherwise. Find the values of u(x,t) at the point x = 4, t = 3. Hint: Let u(x, t)- (x, t) + x sin(t). Write up the equation and the initial condi- tions satisfied by w. Find w(4,3) first 5] Consider the following initial value problem 9utt = uzz-9r sin(t), (x,0) u(x,0' -oo
The joint probability density function for random variables S and T is given by 20,0s 3 10 fk(2s+ for 0 0 otherwis (a) [5 pts] Determine the value of k (b) [5 pts] Find the probability that P(S +T20). Warning: Sketch the integration region.] The joint probability density function for random variables S and T is given by 20,0s 3 10 fk(2s+ for 0 0 otherwis (a) [5 pts] Determine the value of k (b) [5 pts] Find the probability...
Given the initial-value problem ?′′ + 3?′ + 2? = 4?, ?(0) = 3, ?′(0) = 1, Find its homogeneous solution using the Constant Coefficient approach (10pts) Find is particular solution using the Annihilator method. (10pts) Find the general solution that satisfies the initial conditions. (5pts)
[-12 Points] DETAILS Solve the given initial-value problem. 1 -4 -6 X' 2 -3 X, X(0) = 1 1 -2 1 -( W NU -3 X(t) = Submit Answer [-12 Points] DETAILS Solve the given initial-value problem. x = $ =)x, x(0) = -(-3) X(t) =
Given the system transfer f unction: G, (s) -2S+2) S+4 a) Plot the response y(t) for a step input of amplitude 4 for t=[0:0.01:21 b) Verify that the plot is correct using the initial and final value theorems. o) Repeat steps q.and b for G, (s)0S(S + 4). Remember, in input is a step of c) Repeat steps a and b for G2 (S) S+2 amplitude 4.