**First order instrument response to step input:**

The time equation for the step response of a first order instrument is exponential in nature and is given by the equation,

c(t) = 1- ^{−/} .

Where, is called the time constant of the system.

It shows that, the value of the unit step response, c(t) is zero at t = 0 and for all negative values of t. It is gradually increasing from zero value and finally reaches steady state. The steady state value depends on the magnitude of the input.

**Second order instrument response to step input:** The step response of the second order instrument is oscillatory in nature. Depending upon the value of damping ratio, it may be over, under or critically damped or even un- damped.

Fig. below shows the response for an under- damped case. The response up to the settling time is known as transient response and the response after the settling time is known as steady state response. Analysis of such a system is done by calculating different parameters called time response specifications.