This is a really urgent question!

If x=Acos2 pie ft,
then how does f affect x?

sinusoidally, according to the equation.

Increase the frequency f, and x cycles faster.

I'm a little confused. I thought x was displacement. If any side of the right part of the equation is increased, obviously so is the left. Then, wouldn't displacement be increased? Ie---the total "distance" covered? (Yes, I know it osciallates back and forth, and thus in a given time, increasing frequency will increase how fast it cycles.)

"x cycles faster" incorporates time... do you say that because the equation is x as a fuction of t? Would it be wrong to simply say, "as frequency increases, so does displacement," and just leave it at that?

No, because the f and t are inside the cos. X can be 0 at a given f, depending on t.

It would be easier to see if the original equation had been written out properly:



Here t is time (typically seconds), f is frequency (cycles/second), A is the amplitude (meters), and x(t) is the displacement as a function of time. You can see that this function cyces from -A to +A in a sinusoid pattern at a frequency of f cycles per second. Increasing f does nothing to the maximum value that x(t) can reach.

The formula looks clear

Yeah... that makes sense. I think I was confusing amplitude and disp. Thanks.