Sinusoidal Variations

Abstract

Reference has been made, in dealing with oscillatory systems, to quantities which vary sinusoidally with time at a certain frequency. This form of variation is extremely common; the vast majority of domestic and industrial supply voltages, for example, have a waveform which can be expressed in mathematical terms

$$v = {V_m}\sin \omega t$$

as where ω is a constant known as the angular frequency of the voltage wave. (Figure 4.1.) From the diagram it can be seen that the voltage reaches its maximum value when the time t ₁ is such that

$$\omega {t_1} = \pi /2$$

or when

$${t_1} = \pi /2\omega $$

.