Prof. Raghuveer Parthasarathy
University of Oregon; Fall 2007
NAME
:
SOLUTIONS
Physics 351 – Vibrations and Waves
MIDTERM EXAMINATION
Format:
Closed book; no calculators.
Four
problems.
Time:
50 minutes.
(Suggested times: #
1
, 5 min; #
2
, 10 min., #
3
& #
4
, each 15-20 min.)
Write clearly!
You may make use of the following if needed:
For the steady state response of a damped oscillator driven at angular frequency
ω
:
The amplitude (
A
) and phase offset (
δ
) are given by:
(
)
(
)
0
1
2
2
2
2
2
0
2
2
0
/
)
;
tan
(
)
(
F
m
A
γω
ω
δ ω
ω
ω
ω
ω
γω
=
=
−
⎡
⎤
−
+
⎢
⎥
⎣
⎦
The power absorbed (averaged over one cycle):
1
2
2
0
0
0
2
0
(
1
)
2
F
kQ
Q
P
ω
ω
ω
ω
ω
ω
−
⎡
⎤
⎛
⎞
⎢
⎥
=
−
+
⎜
⎟
⎢
⎥
⎝
⎠
⎣
⎦
As usual:
m
is the mass;
k
is the spring constant.;
γ
is the damping factor (“=
b
/
m
”)
ω
0
is the angular frequency of the undamped system.
F
0
is the amplitude of the driving force

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