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A first order linear instrument has an output which is given by a non-homogeneous first order linear differential equationtau.dy(t)/dt + y(t) = K.x(t),
where tau is a constant, called the time constantof the instrument.
In these instruments there is a time delay in their response to changes of input. The time constant tau is a measure of the time delay.
Thermometers for measuring temperature are first-order instruments. The time constant of a measurement of temperature is determined by the thermal capacity of the thermometer and the thermal contact between the thermometer and the body whose temperature is being measured.
A cup anemometer for measuring wind speed is also a first order instrument. The time constant depends on the anemometer's moment of inertia.
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