The rst derivative function time becomes and kdv becomes ksv



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).
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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  �  � 


Solution
V s ( )  �  RCsV C  ( )  � 

V C( )�  1  


RCs  �  1 
The above equation thus describes the relationship between the input and output of the
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