ECEN/MAE 3723 Systems I
Fall 2006
Homework Assignment #7
Problem 1
: Given an electrical circuit shown below, the voltage source
E
is suddenly
connected by means of switch
S
at
t
=
0 . Assume that capacitor
C
is initially uncharged
and that inductance
L
carries no initial current. What is the current
i t
(
) for
t
>
0 ?
Problem 2
: Derive the transfer function
E
s
E
s
o
i
( )
( )
of the electrical circuit shown
below. Then obtain the response
e
t
o
(
) when the input
e
t
i
(
) is a unit step of
magnitude
E
i
(i.e.,
e
t
E u t
i
i
( )
( )
=
). Assume that the initial charge in the capacitor is zero.
Problem 3
: Derive the transfer function
E
s
E
s
o
i
( )
( )
of the electrical circuit shown
below. Then obtain the response
e
t
o
( )
when the input
e
t
i
( )
is a unit step of
magnitude
E
i
(i.e.,
e
t
E u t
i
i
( )
( )
=
). Assume that the initial charge in the capacitor is zero.
Problem 4
: Consider the mechanical system shown below, where
1
1
=
k
N/m,
2
2
=
k
N/m,
5
0
1
.
=
b
N-s/m, and
1
2
=
b
N-s/m. Obtain the response
)
(
t
x
o
when
)
(
t
x
i
is a unit-step displacement input.

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