Diracs delta function examples
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Dirac Delta and Unit Heaviside Step Functions - Examples with Solutions
Table of Contents
The Dirac delta function \( \delta(t) \) and the Heavisisde unit step function \( u(t) \) are presented along with examples and detailed solutions.
Diracs delta function examples
These two functions are used in the mathematical modelling of various engineering systems. Some examples in modelling the responses of electric circuits to unit step voltages are included.
\( \)\( \)\( \)Heaviside Unit Step Function \( u(t) \)
The unit Heaviside step function written as \( u(t) \) (also called Heaviside function and written as \( H(t) \) ) is defined as follows
\( u(t) = \begin{cases} 0 & \text{for } t \lt 0 \\ 1 & \text{for } t \ge 0 \\ \end{cases} \)
which therefore leads to
\( u(t - t_0) = \begin{cases} 0, & \text{for } t \lt t_0 \\ 1, & \text{for } t \ge t_0 \\ \end{cases} \)
One of the main uses of the step function is to model a switch for example.
Suppose we need to apply a voltage \( v(t) \) to a circ