1 Problem You are given the following data (below) showing the steady-state output response, x(t), of a mass-spring-damper (stable, LTI) system to a sinusoidal input u(t) = A sin(wt). This snapshot is the response after all the transients have decayed (the time is shifted to start at zero for conve- nience). x 0.5225 Displacement pu(t) Sinusoidal force input x 0.1041 1.5 1 Y2 х 0.2783 Y1.372 0.5 h ok -0.5- -1 -1.5 x(t) M Assume: bl u(t) x(t) Horizontal Plane (no gravity) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Time (sec) www k Using only the data provided above (the blue line is the input u(t) and the red line is the output x(t)), determine: 1. The frequency of the input in rad/s 2. The amplitude of the input, A 3. The frequency of the output in rad/s 4. The output-input ratio |G(iw)| = max(x(t)) max(u(t))' at the particular input frequency shown. 5. The phase (also called phase lag) of the output, $, at the particular input frequency shown in degrees. Note the phase is generally negative since the output lags behind the input. 6. An analytical expression for the steady-state response, x(t), at the particular input fre- quency shown.
1 Problem You are given the following data (below) showing the steady-state output response, x(t), of a mass-spring-damper (stable, LTI) system to a sinusoidal input u(t) = A sin(wt). This snapshot is the response after all the transients have decayed (the time is shifted to start at zero for conve- nience). x 0.5225 Displacement pu(t) Sinusoidal force input x 0.1041 1.5 1 Y2 х 0.2783 Y1.372 0.5 h ok -0.5- -1 -1.5 x(t) M Assume: bl u(t) x(t) Horizontal Plane (no gravity) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Time (sec) www k Using only the data provided above (the blue line is the input u(t) and the red line is the output x(t)), determine: 1. The frequency of the input in rad/s 2. The amplitude of the input, A 3. The frequency of the output in rad/s 4. The output-input ratio |G(iw)| = max(x(t)) max(u(t))' at the particular input frequency shown. 5. The phase (also called phase lag) of the output, $, at the particular input frequency shown in degrees. Note the phase is generally negative since the output lags behind the input. 6. An analytical expression for the steady-state response, x(t), at the particular input fre- quency shown.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Transcribed Image Text:1 Problem
You are given the following data (below) showing the steady-state output response, x(t), of a
mass-spring-damper (stable, LTI) system to a sinusoidal input u(t) = A sin(wt). This snapshot
is the response after all the transients have decayed (the time is shifted to start at zero for conve-
nience).
x 0.5225
Displacement
pu(t)
Sinusoidal
force input
x 0.1041
1.5
1
Y2
х 0.2783
Y1.372
0.5 h
ok
-0.5-
-1
-1.5
x(t)
M
Assume:
bl
u(t)
x(t)
Horizontal Plane
(no gravity)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Time (sec)
www
k
Using only the data provided above (the blue line is the input u(t) and the red line is the
output x(t)), determine:
1. The frequency of the input in rad/s
2. The amplitude of the input, A
3. The frequency of the output in rad/s
4. The output-input ratio
|G(iw)|
=
max(x(t))
max(u(t))'
at the particular input frequency shown.
5. The phase (also called phase lag) of the output, $, at the particular input frequency shown
in degrees. Note the phase is generally negative since the output lags behind the input.
6. An analytical expression for the steady-state response, x(t), at the particular input fre-
quency shown.
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