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**Unformatted text preview: **teady state for the same system with ζ = 1 .
(a) True (iii) (b) False (b) False The time to reach steady state for an underdamped second order system is a function of the
damping ratio ζ .
(a) True (b) False
Page 2 of 8 Name: __________________________________ Problem 4 [3 points] In a measurement system, repeated measurements can be used to quantify random errors
provided that the unknown input is constant.
(a) True (b) False Problem 5 [3 points] In experimental analysis, a large number of repeated measurements of the unknown input is
taken under the same conditions. The standard deviation is an indication of how spread the
measurements around the mean.
Small standard deviation implies that the instrument used is accurate.
(a) True (b) False Problem 6 [5 points] Consider the periodic signal shown in Figure 1. The Fourier series representation
of this signal is given by f T 0 (t ) = a0 + ∞
n =1 an cos(2π nf 0t ) + b n sin(2π nf 0t ) The coefficient a0 is equal to
(a) a0 = 0;
(b) a0 = 0.25; fT0(t) (c) a0 = 0.5;
(d) a0 = 1.0;
(e) a0 = 2.0. 0.5
0.5 −0.5 −1 t (sec) 1
Figure 1 $( ) *$ $ $ + Page 3 of 8 Name: __________________________________ Problem 7 [5 points] Consider the periodic signal shown in Figure 2. The Fourier series
representation of this signal (a) has a dc component (or average) equal to zero;
(b) contains cosines but not sines;
(c) contains sines but not cosines;
(d) does not contain sines nor cosines;
(e) can not be determined from the given information. ,
$(
.
#$
( (#
( (# - #$
% )$. ( (#
% Figure 2
Problem 8 [10 points] A thermometer, initially at a temperature of 35°C, is suddenly immersed
at t = 0 in a tank of water with a temperature of 70°C. Assume that the thermometer has first
order dynamics with time constant τ = 0.5 sec.
(i) The temperature of the thermometer as a function of time for t ≥ 0 is (a) Tm (t) = 35 ( 2 − e −t / 2 ) o C ; (
(c) T (t) = 35 (1 − 2e
(d) T (t) = 35 (1 − 2e
(e) T (t) = 70 (1 − e (b) Tm (t) = 35 2 − e −2t
m m o )
) −...

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