Consider the two circuits show above, the one on the left is an RCL series
circuit with input and output , while the one on the right is
an RCL parallel circuit with input and output . These two
electrical systems are not equivalent, as they are described by different
governing equations:

and

In general, the canonical form of a general 2nd order system is

where and are the input and output, respectively, and and are the two parameters that describe any 2nd order system. Comparing the canoncal form with two equations above we see that:

and

Note that we also have:

- Steady State Response and Resonance
- Frequency Response Functions of 2nd Order Systems
- Homogeneous Solution
- Complete Solution with Step Input

Ruye Wang 2014-03-23