MAE 350 Midterm 1 S20 Sol.pdf - Rutgers University...

1
Rutgers University
Department of Mechanical and Aerospace Engineering
14:650:350 Mechanical Engineering Measurements
Spring 2020
Midterm 1 Solution
Problem 1:
(a)  = 2 200 Hz
s m
f f
(b) The Nyquist frequency is 50 Hz, so there is no alias frequency for the 40 Hz
component. For the three frequency components:
60 Hz → 40 Hz (out-of-phase)
80 Hz → 20 Hz (out-of-phase)
100 Hz → 0 Hz.
The reconstructed signal is
     = − + = − ( ) sin80 2sin80 3sin40 3sin40 sin80 x t t t t t t
Problem 2:
(a) For the transducer:
The zero-order uncertainty can be calculated as
( )
0
1
0.01 0.005 mm
2
T
u =  =
The linearity error can be calculated as
1% 2 0.02 mm  =
The sensitivity error is 0.02 V=0.02V/(2V/1 mm) 0.01 mm =
The zero-offset error is 0.01 mm
The instrument uncertainty is
( )
2 2 2
0.02 0.01 0.01 =0.0245 mm
C
T
u = + +
The design-stage uncertainty is
( )
( ) ( )
2 2
= 0.025 mm
D L K
T
T T
u u u = + .
(b) For the voltmeter
The full-scale range is 10 mm, which is equivalent to 20 V.
The quantization error is
( )
0
1
0.039 V
2
FSR
M
V
E
u
+
= =
The conversion error is
( )
0.02 V
C
V
u =
The design-stage uncertainty is
( )
( ) ( )
2 2
= 0.044 V
D L K
V
V V
u u u = + .