The function x(t) satisfies the ODE with initial conditions x(0) = 0, x(0) = 0 and X(s) = (a) Find the Laplace Transform X(s) of x(t). = 3/s(s+4)^2 * + 8x + 16x p= 3 s(s+4)² Write down the function f(t). f(t) = (b) The solution x(t) can be written in the form 3, Φ 0 2. f(t) – f(t− 2)H(t − 2)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
The function x(t) satisfies the ODE
with initial conditions x(0) = 0, x(0) = 0 and
(a)
X(s) = 3/s(s+4)^2
Find the Laplace Transform X(s) of x(t).
x + 8x + 16x = Φ
= {³;
{3; 0×152,
t> 2.
3
s(s+4)²
Write down the function f(t).
f(t) =
(b)
The solution x(t) can be written in the form
f(t) = f(t−2)H(t - 2)
Transcribed Image Text:The function x(t) satisfies the ODE with initial conditions x(0) = 0, x(0) = 0 and (a) X(s) = 3/s(s+4)^2 Find the Laplace Transform X(s) of x(t). x + 8x + 16x = Φ = {³; {3; 0×152, t> 2. 3 s(s+4)² Write down the function f(t). f(t) = (b) The solution x(t) can be written in the form f(t) = f(t−2)H(t - 2)
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