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ASE 369K Exam 1
July 5 3,2004
Do not write your name on your exam!
INSTRUCTIONS:
Closed book, closed notes. Equations for first-order, second-order.
and Fog-decrement analysis procedures are provided.
Answer questions in the space provided. If you need to continue
the solution, write on your own paper and staple added sheets to
the back of the exam CJqarlv notc that the solution is continued.
Scoring
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ASE 369K Exam I (7II3/2004)
Frob. 1.
( I 5%)
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Repeated tests of an item of k n o w magnitude (xm,) yields multiple
measurements of the magnitude (x,,,).
(a) I f the repeated measurements are consistently different from the
known or tnre value (i.e., the difference (xm, - x,,~) is
essentially constant)
this error is classified as
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(b) If the repeated measurements are randomly different Fromthe known
or true value, (xm, - x),
js crassified as /
(c) A high precision instrument yields excellent repeat ability and thus
guarantees highl!
ate measurements without calibration (Truc or
False)? Fu'.5A . I,
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. (a) In calibration tcsting, a load cell is found to yield a change of 10 mV
output when the cell i s subiected to an Encremcntal Ioad of 1000
pounds. What is tllc sensitivity ofthe load cell?
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(b) I-tow many independent constants (defining coefficients in the
differential cquation) are required to fully characterize the response of
a firs,t order measurement s q e m ? What are they named?
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(c) Provide a definition for the term "Frequency Response Function.''
Also write the equation for thc Frequency Rcsponsc Function of a
second order mcasurernc~itsystcrn. Define all symbols used in
w i t ing this cquat ion.
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ASE 369K Exam 1 (7/13/2004)
Prob. 3.
(20%)
P 2-
A pendulum is proposed to be used os the primary sensor to measure the
centrifugal force produced by a constant speed centrifuge. The fornula
proposed to quantie this measurement i s
Uncertainty in the mass (m)is 3%, uncertainty in the pendulum length (L)
is 2 %, and uncertainty in the period (T) is 3%.
What js the expeded uncertainty in the measurement of F?
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P 3.
ASE 369K Exam 1 (7/13/2004)
A first order instrument with a time constant of 20 rns is to be used to
measure a periodic (sinusoidal) input. If a dynamic enor of (+I-)10% can
k talernted:
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(a) Determine the maximum frequency of the periodic input that can Ix
acceptably measured. Sketch thc frequency response and identify
frequency range for acceptable use,
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(b) R b t is the associated phasc shiA (angle) at this nlavimurn allowed
frequency'?
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ASE 369K Exam 1 (7J1312004)
d
/+'rob, 5
6 5 (25%)
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P. 4
A transducer that rcsponds as a second-order instrument has a damping
ratio (fraction of critical damping) of 0.5 and an undamped natural
frequency o f 1000 Hz.It is to be used to measure a signal containing
frequencies as high as 750 Hz.
(a) If a dynamic error (amplitude error) of ( 4 - 1 P 0% can k 'tolerated. is
this transducer acceptable?
(b) If the answer to (a) is no. what would k an acceptable fiequcncy
range to limit nleiisurernent of the signal? ~lterl-ratelyif t hc answer (a)
is yes, hat is Ihc cxpected error in the measured amplitude a t a
Crcquency of 750Hz3pecjfv which option i s used.
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