using the Laplace transform solve the IVP
y'' +4y= 3sin(t) y(0) =1 , y'(0) = - 1 , i am stuck on the
partial fraction decomposition step. please explain the
decomposition clearly.
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)=
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 < 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
Solve the IVP:
u'' + 10u' + 98u = 2sin(t/2)
u(0) = 0
u'(0) = 0.03
and identify the transient and steady state portions of the
solution.
Plot the graph of the steady state solution.