A second order system is defined as a system whose input-output relationship can be described by a second order differential equation. Second order systems are important because they are simple yet can exhibit oscillations and overshoot. They also form the basis for higher order systems. As an example, a manometer can be modeled as a second order system, where the pressure difference applied relates to the manometer reading through momentum balance equations that yield a second order differential equation. Damping factors determine if the system is underdamped and oscillatory, overdamped and non-oscillatory, or critically damped for the most rapid response without oscillation.

1. Definition of 2nd order system
A system whose input-output equation is a second order differential equation is
called Second Order System. There are a number of factors that make second order
systems important. They are simple and exhibit oscillations and overshoot.
Higher order systems are based on second order systems.

2. Example of 2nd order system
• Consider a simple manometer. The pressure on both legs of the
manometer is initially the same. The length of the fluid column in the
manometer is L. At time t = 0, a pressure difference is imposed across
the legs of the manometer. Assuming the resulting flow in the manometer
to be laminar and the steady-state friction law for drag force in laminar
flow to apply at each instant, we will determine the transfer function
between the applied pressure difference ∆ P and the manometer reading
h. If we perform a momentum balance on the fluid in the manometer, we
arrive at the following terms:
• (Sum of forces causing fluid to move = Rate of change of momentum of
fluid)-----eq-1

3. Manometer figure
• Figure 7-1 as mentioned in book chapter no. 7 . Book is already
shared with you

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8. • If damping factor>1 over damped system means non oscillatory
• If damping factor =1 critical damped system which allows most rapid
approach to response with oscillation.