Find the laplace transformation for the given function. 1. (t1)u (t1) е 2и (t - 1)...
find the laplace transformation and the region of converge of the following functionu(t)-u(t-1)
Problem 2. In each part below, either diagonalize the given linear transformation, if possible, or else explain why this is impossible. (That is, find a basis B such that the coordinate matrix [T\B or explain why no such basis exists.) (а) Т: Р2 —> Р2 given by T(p) — ар'. (b) Т:P, — P2 given by T(р) — р(2л — 1). (c) T R2x2 R2x2 given by T(A) = A+ AT. (d) T: С +С given by T(a + bi)...
1. Find the Laplace transforms of these functions: r(t) = tu(t), that is, the ramp function; Ae-atu(t); Be atu(t). 2. Determine the Laplace transform of f(t) = 50cos ot u(t). 3. Obtain the Laplace transform of f(t) = (cos (2t) + e 41) u(t). 4. Find the Laplace transform of u(t-2). 5. Find vo(t) in the circuit shown below, assuming zero initial conditions. IH F + 10u(i) 42 v. (1)
Solve the IVP using laplace transformation y”+3y=(t-2)u(t-1) y(0)=-1 y’(0)=2 Solve the IVP usiag laplace transformahbn 3y (t-2) u (t-1) (0) 2 yo)-1 Solve the IVP usiag laplace transformahbn 3y (t-2) u (t-1) (0) 2 yo)-1
Find the Laplace Transformation of the following function.f(t) =
find the laplace transformation of the following functiona) u2(t) (t2 +5t -3 )b) u3(t)te2t
Question 2: (26 marks) 2.1 Find the The Laplace transform of the following function t, if 03t<1 2t, if t1 [3] 2.2 Find the inverse Laplace transform of 10e 2 52 - 53 +632 - 25 + 5 (10] 2.3 Find y(4) if y(t) = u(t){t - 2)2 - us(t)/(t - 3) - 2) - us(t)e' (51 2.4 Solve the following initial value problem given by y" + 4y = 28.(t) (0)=1/(0) = 0 181 Question 3: (17 marks) Let...
find the laplace transformation of the solution of the ivpy''- 3y' + 2y = u1(t)e^(4t )y(0) = 1, y'(0 ) = 2
Find the Laplace transform of the function f(t). f(t) = sint if o St<$21; f(t) = 0 if t> 21 Click the icon to view a short table of Laplace transforms. F(S) =
1-5 im struggling pls help Applications of Solutions by Laplace Transform Given L I (0) = 0 for t > 0. Solve for the current I (t) +臘娃q=E(t), w th L-1h,R= 20 ohms, C=0.005 f, E(t) = 150V, q(0)=0and 1. de? Find the charge q(t) in an RC series circuit when q(0)-0 and E(t) = E e-kt, k > 0. Consider both when k 2. and when k = RC. Translations on the t-Axis Using Unit Step Function Find the...
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