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 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
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)=
Solve the following IVP specifically using the Laplace transform
method
(d^3)x/d(t^3)+x=e^(-t)u(t) f(0)=0 f'(0)=0
f''(0)=0
where u(t) is the Heaviside step function
Use the Laplace transform to solve the following initial value
problem:
?″+6?′+58?=?(?−4)
?(0)=0,?′(0)=0
(Notation: write u(t-c) for
the Heaviside step function ??(?)uc(t) with step at ?=?t=c.)