A harmonic input signal is sent into a system which is knowm to be 1st order a)
ID: 2291920 • Letter: A
Question
A harmonic input signal is sent into a system which is knowm to be 1st order
a) Determine the parameters, A and ?f, of the input signal such that f(t) = Acos(?f t).
b) Approximately how long a time does it take before the transient response dies out?
c) What is the frequency of the response? How does it compare to ?f ?
d) Determine the magnification factor of the steady-state behavior (MF = ratio of response magnitude to input signal magnitude).
e) Determine the phase shift of the steady-state response to the input. Indicate if the response if lagging or leading.
f) Determine the time constant of the system.
g) Determine the static gain of the system.
h) Identify the initial condition.
i) Write the DE model of the system.
j) Write down the analytical solution of this DE. Identify the transient and steady-state terms of the analytical solution.
Input fit)-Acos(wt) Response x(t) Unknown 1st-order Both the input signal and the response are shown on the plot below nput Response 1.5 0.5 0.5 -1 1.5 0 02 04 06 08 12 1.4 16 182 22 24 26 2 3 32 34 36 3s4 time 1.9 1.8 1.7 Response 1.5 1.4 1.3 1.2 0.9 08 0.7 0.6 0.5 3 3.05 31 315 32 3.25 33 335 3.4 345 35 356 3.6 time [s)Explanation / Answer
Hello,
Please find the answer attached as under. Please give a thumbs up rating if you find the answer useful! Have a rocking day ahead!
(a) A = 2 and time period = 1.6 secs. Thus, f = 1/T = 0.625 Hz
(b) The transient response dies out after approximately 1.2 secs
(c) The frequency of the response is also 0.625 Hz = f.
(d) Magnification factor = Vout/Vin = 0.9/2 = 0.45
(e) The response is lagging by t = 1.9-1.6 secs = 0.3 secs = 2*pi*f*t = 2*pi*0.625*0.3 = 1.17 radians
(f) Time constant = T and 5T = transiet settling time. Therefore, 5T = 1.2 secs. Thus, T = 0.24 secs
(g) Static gain = magntiude ratio = 0.45
(h) Initial condition is y(0) = -1
For the last 2 questions, could you elaborate on what 'DE' means...
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.