Response of First-Order Systems and Time Constant Problem: Find the free-vibration response and the time constant, where applicable, of systems governed by the following equations of motion: (Note: The time constant can also be defined as the value of time at which the step response of a system rises to 63.2% (100.0% — 36.8%) of its final value.)

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Response of First-Order Systems and Time Constant Problem:

Find the free-vibration response and the time constant, where applicable, of systems governed by the following equations of motion:

(Note: The time constant can also be defined as the value of time at which the step response of a system rises to 63.2% (100.0% — 36.8%) of its final value.)

a. 100i + 20v = 0, v(0) = v(t = 0) = 10
b. 100i + 20v = 10, v(0) = v(t = 0) = 10
c. 100i – 20v = 0, v(0) = v(t = 0) = 10
d. 500à + 50w
%3D
%3D
0, w(0) = w(t = 0) = 0.5
%3D
%3D
Transcribed Image Text:a. 100i + 20v = 0, v(0) = v(t = 0) = 10 b. 100i + 20v = 10, v(0) = v(t = 0) = 10 c. 100i – 20v = 0, v(0) = v(t = 0) = 10 d. 500à + 50w %3D %3D 0, w(0) = w(t = 0) = 0.5 %3D %3D
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