The graphing window shows two sinusoids. A reference sinusoid in cyan and a transformed sinusoid in yellow. The reference sinusoid is the graph of \(y(t) = \cos(\omega t)\). That is, it has amplitude \(1\) and phase lag \(0\). The transformed sinusoid is \(f(t) = A\cos(\omega t - \phi)\). That is, it has the same angular frequency as the reference, but different amplitude and phase lag.

The values of amplitude \(A\), phase lag \(\phi\) and angular frequency \(\omega\) are all settable using the corresponding sliders.

The values of the time lag \(t_0\), period \(P\) and frequency \(\nu\) are shown at the right below the graphing window. Time lag is the time between the first maximum of the reference sinusoid and the first maximum of the transformed sinusoid. This is also indicated by the green lines on the graph. The period is also indicated by the orange lines on the graph. Being careful with terminology: the angular frequency \(\omega\) has units of radians per unit time and the frequency \(\nu\) has units of cycles per unit time. Of course, the relationship is \(\omega = 2\pi\nu\).

© 2018 J. Orloff and H. Miller using the DAIMP Libraries