Find the Laplace transform of the given function. (Express your answer in terms of s. Assume...

Find the Laplace transform of the given function. (Express your answer in terms of s. Assume that

s > 0.)

f(t) =

0,	t < 1
t² − 2t + 4,	t ≥ 1

Expert Solution

milcah answered 2 years ago

Find the inverse Laplace transform for 1 / ((s^2+1)(s+1))

What are the advantages of using Laplace transform? Justify your answer

Find the Laplace transform of d2y/dt2

find inverse laplace transform of F(s)= (2s³ +5s²+8s+22)/[(s²+4)(s²+3s+2)]

Use a table to find the inverse Laplace transform h(t) of H(s). H(s) = 40s /((s2...

Use a table to find the inverse Laplace transform h(t) of H(s). H(s) = 40s /((s2 + 4)(s + 1)) for s > 0 h(t) = for t > 0

Find the energy U0 stored in the capacitor. Express your answer in terms of A, d, V, and ϵ0.

Part A Find the energy U0 stored in the capacitor. Express your answer in terms of A, d, V, and ϵ0. Remember to enter ϵ0 as epsilon0. Part B The capacitor is now disconnected from the battery, and the plates of the capacitor are then slowly pulled apart until the separation reaches 3d. Find the new energy U1 of the capacitor after this process. Express your answer in terms of A, d, V, and ϵ0. Part C The capacitor is...

Use the Laplace transform to find the solution of the IVP: a.) 2y' + y =...

Use the Laplace transform to find the solution of the IVP: a.) 2y' + y = 1, y(0) = 2 (answer should be y(t) = 1 + e-t / 2 ) f.) 4y" + y = 0, y(0) = -1, y'(0) = -1 (answer should be y(t) = -sin(t) - cos(t)) Please show work!

1) Find the Laplace transform of f(t)=−(2u(t−3)+4u(t−5)+u(t−8)) F(s)= 2) Find the Laplace transform of f(t)=−3+u(t−2)⋅(t+6) F(s)=...

1) Find the Laplace transform of f(t)=−(2u(t−3)+4u(t−5)+u(t−8)) F(s)= 2) Find the Laplace transform of f(t)=−3+u(t−2)⋅(t+6) F(s)= 3) Find the Laplace transform of f(t)=u(t−6)⋅t^2 F(s)=

Find the Laplace transform of the following functions. (a) f (t) = { 6 0 < ...

Find the Laplace transform of the following functions. (a) f (t) = { 6 0 < t ≤ 4 8 t ≥ 4 (b) f (t) = { t2 0 ≤ t < 3 0 t ≥ 3 (c) f (t) = { 0 0 ≤ t < π/4 cos[7(t − π/4)] t ≥ π/4

1. Find the solution by using the Laplace transform. a) y ′′ + 2ty′ −4y =...

1. Find the solution by using the Laplace transform. a) y ′′ + 2ty′ −4y = 1 , y(0) = y ′ (0) = 0

Question