2-39 Describe the following functions for t > 0. a. i(t) = 10e-2 sin 2 mrt...
1) Given the functions xi()-tu()-tu(t-I) and xz()-10e "u(), do the following: Find x()-x(0)*xz() by hand using Laplace transforms. 1) Given the functions xi()-tu()-tu(t-I) and xz()-10e "u(), do the following: Find x()-x(0)*xz() by hand using Laplace transforms.
3. Let z,-34J4 and z2-10e'. Find the results of: zit 22,21 * 22,21/22, ะ?, and å . Find the Laplace transforms of the following functions: note that t2 0 1). f(t) =e®.4tcos 12t. f) sin(t 3), f(t) =cos2wtcos3wt. Hint: You may want to use the following identities: cos(o + β)-cosoosß-sino sind, sin θ = , 2 2j 3. Let z,-34J4 and z2-10e'. Find the results of: zit 22,21 * 22,21/22, ะ?, and å . Find the Laplace transforms of the...
3) The switch moves from position a to b at time t-0. Find i(t) for t >0 a 62 i(t) b 3 2 108 V (t 2 H
TT If sin sin (m) cos(0) and 0° < 2. t then 2 =
Given the network in fig., find v(t) for t>0. 2 A 1 H 4Ω 6 A 1Ω 0.03 F v (t) = cos sin
1. [10pts) Find it) and (t) for 1> 0 in the circuit below if i(0) - 10 A. iſt) 32H § 202 { v(t) 310
Problem 1: Find i(t) and v(t) for all time. 50 t=0 t=0 W 200 mF 1022 3A 20 V +1 А i(t) = 0A, v(t) = 20V B i(t) = 0A, v(t) = 30 – 10e-t/2v с i(t) = 3A, v(t) = 30e-t/2V D i(t) = 0A, v(t) = 10e-t/2v
Are the following functions concave, convex, or neither for x > 0? (i) f(z) =ztt convex, (i) f (x)x -2 (iii) f (x) = x In x (iv) f (x)-/Inr (v) f (x) = min(x2, x3}
1. Consider the curve i(t) = (t sin(t) + cos(t))i + (sin(t) – t)j + tk. (a) Find the length of the curve for 0 <t<5. (b) Is the curve parameterized by arc length? Justify your answer. (C) If possible, find the arc length function, s.
P4.67 Solve for i(t) for t > 0 in the circuit of Figure P4.67 with R-500. given that i(0+) 0 and v(0+) 20 V. [Hint: Try a particular solution of the form (1) = A cos(100r) B sin(100r).] t=0 I H 20 sin(1001) i(t) It(r) 100 ?F Figure P4.67