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The rst derivative function time becomes and kdv becomes ksv


Chapter 18

2. A constant k which does not vary with time remains a constant. Thus kv , where v is a function of time, becomes kV(s). For example, the voltage 3 v written as an s function is 3 V(s).

3. If the initial value of the variable v is zero at time t� 0, the fi rst derivative of a function of time dv/dt becomes sV(s) and kdv/dt becomes ksV(s). For example, with no initial values 4dv/dt as an s function is 4sV(s).

Control and Instrumentation Systems

With an integral of a function of time:


v d becomes 1
s V s ( )
kv d becomes

into an s function.

Example 18.14


v C


V s ( ) RCsV C ( )
V C( )� 1

V s ( )

RCs 1

The above equation thus describes the relationship between the input and output of the

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the rst derivative function time becomes and kdv b
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