Find the laplace transform of the following functions, using the definition of Laplace transforms: f(t)=-2cos4t f(t)=2...

Find the laplace transform of the following functions, using the definition of Laplace transforms:

f(t)=-2cos4t

f(t)=2 sin^2(t)

g(t)=3e^tcos(t)

Expert Solution

Colby Messinger answered 1 year ago

1. Find the Laplace transform of each of the following functions: (a). f(t) = t ,...

1. Find the Laplace transform of each of the following functions: (a). f(t) = t , (b). f(t) = t2 , (c) f(t) = tn where n is a positive integer Laplace transform of the given function 2. . f(t) = sin bt 3. f(t) = eat sin bt

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

Find the Laplace Transform of the functions t , 0 ≤ t < 1 (a) f(x)...

Find the Laplace Transform of the functions t , 0 ≤ t < 1 (a) f(x) = 2 − t , 1 ≤ t < 2 0 , t ≥ 2 (b) f(t) = 12 + 2 cos(5t) + t cos(5t) (c) f(t) = t 2 e 2t + t 2 sin(2t)

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 functions: f(t) = 3e^5t t^3 − 6e^−t t^4 g(t)...

. Find the Laplace transform of the functions: f(t) = 3e^5t t^3 − 6e^−t t^4 g(t) = 5e^3t cos(4t) − 6e^2t sin(7t)

Find the Laplace transforms: F(s)=L{f(t)} of the function f(t)=(8−t)(u(t−2)−u(t−5)), for s≠0. F(s)=L{f(t)}=

Find All the following Laplace Transformations once using the definition of Laplace Transformation and then using...

Find All the following Laplace Transformations once using the definition of Laplace Transformation and then using the memorized Laplace Table relationships: L[sin⁡(ω*t)] L[(e-5t)cos⁡(6t)] L[(e-5t)(t2)]

Use Laplace Transforms to solve the following IVPs . y′′+9y={2−t ,0} piecewise function 0≤t<2 , t≥2...

Use Laplace Transforms to solve the following IVPs . y′′+9y={2−t ,0} piecewise function 0≤t<2 , t≥2 ;y(0)=1 ,y′(0)=0

Use Laplace transforms to solve x''− 7x' + 6x = e^t + δ(t − 2) +...

Use Laplace transforms to solve x''− 7x' + 6x = e^t + δ(t − 2) + δ(t − 4), x(0) = 0, x'(0) = 0.

inverse laplase transform problem F(s)= (7s+11)/s(s+5)((s^2)+4s+20) find F(t) using laplase transform

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