The period of any wave is the time it takes for its angle to go from zero to 2pi .
The 'sin' function is a wave. The angle of this one is (8pi t).
When t=0, the angle is zero. Wonderful. Now, how long does it take for the angle to grow to 2pi ?
I*n other words, when is (8pi t) = 2pi ?
Divide each side by '2pi': . . . . . 4 t = 1
Divide each side by ' 4 ': . . . . . t = 1/4
And there you are. Every time 't' grows by 1/4, (8pi t) grows by 2pi. So if you graph this simple harmonic motion described by 'd', you'll see the graph wiggle up and down with a period of 1/4 .
