Impedance analysis is commonly used to analyze electrical circuits [110]. By means of equivalent circuits, we can use the same analysis methods for mechanical systems.
For example, referring to Fig.7.9, the Laplace transform of
the force on the spring
is given by the so-called voltage
divider relation:8.2
Similarly, the Laplace transform of the force on the mass
As a simple application, let's find the motion of the mass
, after
time zero, given that the input force is an impulse at time 0:
Then, by the ``voltage divider'' relation Eq.(7.1), the Laplace transform of the mass force
where we have defined
Thus, the impulse response of the mass oscillates sinusoidally with
radian frequency
, and amplitude
. The
velocity starts out maximum at time
, which makes physical sense.
Also, the momentum transferred to the mass at time 0 is
;
this is also expected physically because the time-integral of the applied
force is 1 (the area under any impulse
is 1).