- #36

- 897

- 176

I have tried to plot the 3 graphs of ##y=sin{x}## in bold black, ## y= sin{2x}## in normal black and ##y=sin{4x}## in bold blue as shown below.kuruman said:So it seems. But are the two the same kind of zero in the sense that ##\sin(\omega t)## crosses the axis going the same way? That's why I suggested that you plot this thing.

It seems that the combination of these 3 graphs will repeat every 360° or 2π radians. We can't say the combination will repeat every 180° or π radians since the graph of ##y = sin x## is inverted after 180° even though the patterns of ## y= sin{2x}## and ## y= sin{4x}## graphs are repeating every 180°. The superposition of multiple graphs depends entirely on the pattern of individual graphs; so, if patterns of graphs do not change then the superposition of these graphs will not change.

From above explanation, we can say that motion is periodic with a time period equal to the time period of ##y= sin {\omega t}## which is ##T= \dfrac {2\pi}{\omega}##.

Last edited: