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).

With an integral of a function of time:

into an s function.

Example 18.14

Solution

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