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dimensional cams have been used in machining fan blade surfaces (Nilson, 1980) and aircraft gas turbine blades (Thompson et al, 1983), and in controlling ow through an ori ce (Mabie and Reinholtz, 1987) Variable valve timing systems used in internal combustion engines have also employed them (Titolo, 1991) The problem of de ning three-dimensional surfaces has been addressed (Dhande et al, 1975; Tsay and Hwang, 1994a, b) The analytical representation of the cam surface can be written as (Tsay and Hwang, 1994a) A cos f - r( B sin f 2 + A cos f 2 ) 2 D x r( B cos f 2 - A sin f 2 ) y = - A sin f 2 D z rAC - s2 - D

// A simple clock using System; class SimpleClock { static void Main() { string t;

Part II:

F (x) (cos x)(sin x)

(534)

int seconds; DateTime dt = DateTimeNow; seconds = dtSecond; for(;;) { dt = DateTimeNow; // update time if seconds change if(seconds != dtSecond) { seconds = dtSecond; t = dtToString("T"); if(dtMinute==0 && dtSecond==0) t = t + "\a"; // ring bell at top of hour ConsoleWriteLine(t); } } } }

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Although the standard date and time format specifiers will apply to the vast majority of situations, you can create your own, custom formats The process is similar to creating custom formats for the numeric types, as described earlier In essence, you simply create an example (picture) of what you want the date and time information to look like To create a custom date and time format, you will use one or more of the placeholders shown in Table 22-8 If you examine Table 22-8, you will see that the placeholders d, f, g, m, M, s, and t are the same as the date and time format specifiers shown in Table 22-7 In general, if one of these characters is used by itself, it is interpreted as a format specifier Otherwise, it is assumed to be a placeholder If you want use one of these characters by itself but have it interpreted as a placeholder, then precede the character with a % The following program demonstrates several custom time and date formats:

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// Format time and date information using System; class CustomTimeAndDateFormatsDemo { static void Main() { DateTime dt = DateTimeNow; ConsoleWriteLine("Time is {0:hh:mm tt}", dt); ConsoleWriteLine("24 hour time is {0:HH:mm}", dt); ConsoleWriteLine("Date is {0:ddd MMM dd, yyyy}", dt); ConsoleWriteLine("Era: {0:gg}", dt); ConsoleWriteLine("Time with seconds: " + "{0:HH:mm:ss tt}", dt);

SOLUTION We have [ln F (x)] = [ln(x 2 (sin x) 5x )] = [(2 ln x) + ln(sin x) + (x ln 5)] 2 cos x + ln 5 = + x sin x Using formula ( ), we conclude that 2 cos x F (x) + ln 5 = + sin x F (x) x

22:

ConsoleWriteLine("Use m for day of month: {0:m}", dt); ConsoleWriteLine("use m for minutes: {0:%m}", dt); } }

idealized elements: point masses or lumped inertias, massless springs that provide force as some function of displacement, and massless dampers that produce force as a function of some velocity in the system Once the properties of the individual components have been identi ed, the individual masses, springs, and dampers can be lumped together to produce simple models of the complete system This process of lumping in many cases requires making judgments about which elements of the system are dominant and which can be ignored For instance, elements with very little compliance can often be assumed rigid and elements with very small mass can often be assumed massless in order to simplify the modeling process The chapter begins by presenting some fundamental concepts from vibrations and system dynamics that prove useful in model reduction and assessment The next three sections treat each of the basic modeling elements mass or inertia elements, spring elements, and dampers individually and discuss the rules for obtaining equivalent elements when multiple elements are lumped or combined The nal section of the chapter applies all of the concepts of modeling, simpli cation, and evaluation to produce a simple model of an automotive valve-gear system

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