EXERCISES 5.1 In addition to the standard inputs discussed in Section 5.1, other input functions occasionally are useful for special purposes. One, the so-called doublet pulse, is shown in Fig. E5.1. (a) Find the Laplace transform of this function by first expressing it as a composite of functions whose transforms you already know. (b) What would be the response of a process having a first-order transfer function K/TS + 1) to this input? of the integrating process K/s? (c) From these results, can you determine what spe- cial property this input offers? *Dp(t) h 0 Figure E5.1 tw 2tw

5.1 In addition to the standard inputs discussed in Section 5.1, other input functions occasionally are useful for special purposes. One, the so-called doublet pulse, is shown in Fig. E5.1. (a) Find the Laplace transform of this function by first expressing it as a composite of functions whose transforms you already know. (b) What would be the response of a process having a first-order transfer function K/(s+1) to this input? of the integrating process K/s ? (c) From these results, can you determine what special property this input offers