
4.3.3 IMPULSE RESPONSE
The response of LTI systems to an impulse forcing function is of great interest. We shall see why
momentarily, but first an example is presented illustrating the process of finding the response of a
simple system to an ‘‘impulse-like’’ input and comparing it with the true impulse response of the
system.
Example 4.8
A spring-mass-damper system is struck by a hammer resulting in a force f(t) like the one shown in
Figure 4.7.
(a) Find and graph the response x(t) for T ¼1, 0.5, 0.1, 0.01 s.
(b) Find and graph the impulse response.
(a) The differential equation model of the system is
m
€
x þ c
_
x þ kx ¼ f )
€
x þ 2
_
x þ 4x ¼
1
T
[
^
u(t)
^
u(t