Is there anywhere on a sine wave that is 'linear' - like, say, where a 'particle' is just 'coasting'? How 'big' is that spot? What are the maths thereof?
2007-12-23 14:59:10 · 3 answers · asked by c0cky 5 in Science & Mathematics ➔ Physics
Sine waves are linear in the sense of having an acceleration of 0 twice in each cycle, but only instantaneously (the derivative of the sine wave is a cosine wave, and the second derivative which is the acceleration is -1 times the original sine wave). Where the sine wave cross the y=0 line, both going up and going down, for that instant the acceleration stops and it is going in a straight line. Just before it is accelerating in one direction, and just after it is accelerating in the opposite
The spot has a length of 0 in both cases.
2007-12-23 15:43:22 · answer #1 · answered by VirtualSound 5 · 0⤊ 0⤋
well, there isn't any point where its linear, but there is an infinitely small part where it is "flat", that is where the derivative is 0, and on a graph is has no slope or rate of change. if you imagine a block on a spring just rocking back and forth you'll have one instant at either end where it will won't be moving as it changes direction.
that math would be finding where the derivative of sine is equal to 0. the derivative of sine is cosine as someone else already stated and cosine = 0 at (n*pi)/2 where n is any odd integer
2007-12-23 17:17:57 · answer #2 · answered by lalowawrzyniec 1 · 1⤊ 0⤋
No, there's not. Use a tangent line.
2007-12-23 15:07:37 · answer #3 · answered by Anonymous · 3⤊ 0⤋