Integration of unit ramp function gives

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Question

This question was previously asked in

UKPSC JE Electrical 2013 Official Paper II (Held on 7 Nov 2015)

Answer 1

Ramp input:

It is a standard input signal that consists of a constant rate of change in input.

The ramp is a signal, which starts at a value of zero and increases linearly with time

$r (t) = {\begin{matrix} A t; t \geq 0 \\ 0; e l s e w h e r e \end{matrix}$

If amplitude A=1, it is called Unit Ramp Input.

The integration of the unit ramp is a parabolic signal

$p (t) = \int t d t = \frac{t^{2}}{2}$

A parabolic signal is expressed as

$p (t) = {\begin{matrix} \frac{t^{2}}{2}; t \geq 0 \\ 0; e l s e w h e r e \end{matrix}$

Important points: