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Questions get repeated sometimes from previous year papers or similar sort of questions are given.This could be helpful.
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EED-201: Assignment 4 (Laplace transform)
i) 𝑋(s) =
s
2
+2s+ 5
(s+ 3 )(s+ 5 )
2
, Re(s) > - 3 ii) 𝑋(s) =
2 𝑠+ 1
s+ 2
, Re(s) > - 2
iii) 𝑋(s) =
𝑠
3
2
𝑠
2
, Re(s) > 0
i) x(t) = cos(𝜔
0
ii) x
t
−𝑎𝑡
𝑎𝑡
iii) x(t) = 𝑠𝑔𝑛(𝑡)
−𝑡
𝑢(𝑡). For a certain
unknown input x(t), the output y(t) is observed to be ( 2 − 3 𝑒
−𝑡
− 3 𝑡
)𝑢(𝑡). Find the input
x(t).
equations:
𝑑𝑥(t)
dt
and
𝑑𝑦
( t
)
dt
Determine X(s) and Y(s) along with their regions of convergence.
Determine a differential equation relating the input x(t) to the output y(t) of this system.
𝐻
( 𝑠
𝑠+ 1
𝑠
2
Determine and sketch the response y(t) when the input is: 𝑥
( 𝑡
) = 𝑒
−|𝑡|
, −∞ < 𝑡 < ∞.