ME3015 Summer 2009
PROBLEM SET #6 (25 points). Document as outlined in the course admin letter.
Due: The beginning of Lesson 30 (July 2nd).
1. (8 points) Consider the following system. Obtain the response )(
1tx and )(
2tx analytically
when u is a unit-step input.
)(
1
0
56
10
2
1
2
1tu
x
x
x
x⎥
⎦
⎤
⎢
⎣
⎡
+
⎥
⎦
⎤
⎢
⎣
⎡
⎥
⎦
⎤
⎢
⎣
⎡
−−
=
⎥
⎦
⎤
⎢
⎣
⎡
&
&
⎥
⎦
⎤
⎢
⎣
⎡
=
⎥
⎦
⎤
⎢
⎣
⎡
0
0
)0(
)0(
2
1
x
x
2. (9 points) Find the natural frequencies for the system below where m1=1[kg], m2=1[kg], k=20
[N/m], a=1[m], L=3[m]. Assume a small angle of motion.
1
θ
2
θ
k
l
a
1
m2
m
g
