Page 340 - Mechanical Engineers' Handbook (Volume 2)

5 Approaches to Linear Systems Analysis 331

Figure 14 Family of singularity functions commonly used as test inputs.

y(t) y [y y ]e t / r
ss
0
ss
where y u is the steady-state response. Table 6 and Fig. 16 record the values of y(t) and
ss
y(t) for t k , k 0, 1,...,6. Note that over any time interval of duration , the response
˙
increases approximately 63% of the difference between the steady-state value and the value
at the beginning of the time interval, that is,
y(t ) y(t) 0.63212[y y(t)]
ss
Note also that the slope of the response at the beginning of any time interval of duration
intersects the steady-state value y at the end of the interval, that is,
ss