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 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)=
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 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)
Consider the differential equation
y′(t)+9y(t)=−4cos(5t)u(t),
with initial condition y(0)=4,
A)Find the Laplace transform of the solution
Y(s).Y(s). Write the solution as a single
fraction in s.
Y(s)= ______________
B) Find the partial fraction decomposition of Y(s). Enter all
factors as first order terms in s, that is, all terms
should be of the form (c/(s-p)), where c is a constant and the root
p is a constant. Both c and p may be complex.
Y(s)= ____ + ______ +______
C)...