(b) Figure Q4(b) shows an electro-mechanical system. The solenoid in the electrical sub- system behaves as an inductor L. The resistor R is connected in series with L in order to limit the current i(t) through the solenoid. Current i(t) energizes the solenoid such that the mass M is displaced to x(t) by the external force f(t). During experimental set-up, inventor tabulates the system parameters in Table Q4(b), and approximates the force-current relationship as f(t) = KAi(t) with KA> 0. Formulate the system's transfer function in order to measure the displacement x(t) due to the input voltage v(t). x(1) i(1) R K O v(1) D M L |D, Figure Q4(b)

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(b)
Figure Q4(b) shows an electro-mechanical system. The solenoid in the electrical sub-
system behaves as an inductor L. The resistor R is connected in series with L in order
to limit the current i(t) through the solenoid. Current i(t) energizes the solenoid such
that the mass M is displaced to x(t) by the external force f(t). During experimental
set-up, inventor tabulates the system parameters in Table Q4(b), and approximates the
force-current relationship as
f(t) = Kai(t)
with KA > 0. Formulate the system's transfer function in order to measure the
displacement x(t) due to the input voltage v(t).
x(1)
i(1) R
K
m
v(1)
M
D
D
Figure Q4(b)
Transcribed Image Text:(b) Figure Q4(b) shows an electro-mechanical system. The solenoid in the electrical sub- system behaves as an inductor L. The resistor R is connected in series with L in order to limit the current i(t) through the solenoid. Current i(t) energizes the solenoid such that the mass M is displaced to x(t) by the external force f(t). During experimental set-up, inventor tabulates the system parameters in Table Q4(b), and approximates the force-current relationship as f(t) = Kai(t) with KA > 0. Formulate the system's transfer function in order to measure the displacement x(t) due to the input voltage v(t). x(1) i(1) R K m v(1) M D D Figure Q4(b)
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