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SOLUTION According to our de nition, ex = exp(x ln(e)) But we learned in the last section that ln(e) = 1 As a result, ex = exp(x) You Try It: Simplify the expression ln[ex x e ] Because of this last example we will not in the future write the exponential function as exp(x) but will use the more common notation ex Thus exp(ln x) = x ln(exp(x)) = x becomes eln x = x becomes ln(ex ) = x

Linear Model of Single DOF System The procedures that are described here are based on the linear, lumped parameter model shown in Fig 523 It is composed of a single mass and massless springs and dampers Such a model is usually satisfactory in addressing the dynamic effects of general camfollower mechanisms (Barkan, 1953; Chew et al, 1983; Freudenstein et al, 1983; Kanzaki and Itao, 1972; Wiederrich and Roth, 1975) Further, follower models consisting of one or two degree-of-freedom systems will be adequate because the dynamic response of most cam-follower systems is dominated by the fundamental frequency and probably the second harmonic of the cam-follower system (Barkan, 1965) In fact, it has been shown (Koster, 1974) that a cam-follower system can be modeled by a single degree-of-freedom system without introducing signi cant errors if the system has a natural frequency equal to the frequency of the actual cam-follower system As a consequence, single degree-of-freedom systems have been studied by most authors (Barkan, 1953; Chen, 1981; Chew et al, 1983; Freudenstein, 1960; Hrones, 1948; Kanesaka et al, 1978; Kanzaki and Itao, 1972; Kwakernaak and Smit, 1968; Mercer and Holowenko, 1958; Rees Jones and Reeves, 1978; Tesar and Matthew, 1976; Wiederrich and Roth, 1975) who have made general investigations of output motions or who have designed cam pro les The general, simple model used in this work is shown in Fig 523 Although it will not be explained here, the single degree-of-freedom can be extended to include nonlinear Coulomb friction damping

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There is one important thing to notice in this output: the empty string that occurs between land and two This is caused by the fact that in the original string, the word land is followed by a comma and a space, as in land, two However, both the comma and the space are specified as separators Thus, when this string is split, the empty string that exists between the two separators (the comma and the space) is returned There are several additional forms of Split( ) that take a parameter of type StringSplitOptions This parameter controls whether empty strings are part of the resulting split Here are these forms of Split( ): public string[ ] Split(params char[ ] seps, StringSplitOptions how) public string[ ] Split(string[ ] seps, StringSplitOptions how) public string[ ] Split(params char[ ] seps, int count, StringSplitOptions how) public string[ ] Split(string[ ] seps, int count, StringSplitOptions how) The first two forms split the invoking string into pieces and return an array containing the substrings The characters that delimit each substring are passed in seps If seps is null, then whitespace is used as the separator In the third and fourth forms, no more than count substrings will be returned For all versions, the value of how determines how to handle empty strings that result when two separators are adjacent to each other The StringSplitOptions enumeration defines only two values: None and RemoveEmptyEntries If how is None, then empty strings are included in the result (as the previous program showed) If how is RemoveEmptyEntries, empty strings are excluded from the result To understand the effects of removing empty entries, try replacing this line in the preceding program:

string[] parts = strSplit(seps);

130 1

with the following:

exp(a + b) = [exp(a)] [exp(b)] becomes ea+b = ea eb exp(a) ea becomes ea b = b exp(a b) = exp(b) e b b ln a b a = exp(b ln a) becomes a = e EXAMPLE 616

string[] parts = strSplit(seps, StringSplitOptionsRemoveEmptyEntries);

[w] [09,1,22,22,1,09] [w] [4,1,1,1,4] [w] [1,1,2,2,1,1]

When you run the program, the output will be as shown next:

Pieces from split: One if by land two if by sea Result of join: One | if | by | land | two | if | by | sea

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