Question

PLEASE HELP ASAP!!!

Answer 1

1Hz = One Cycle   and   One Cycle = 360degrees

When you want to find the difference caused by a time separation of two waves, you can find how much of a wave cycle will pass during the time delay.

At 0.25Hz, it takes 4 seconds to make 1 Cycle. With some algebra you find that 1 cycle every 4 seconds = a quarter cycle every 1 second.

So now that you know a one second delay causes a quarter of a cycle to pass, you can convert that into degrees by multiplying 0.25 and 360.   0.25x360=90

Lo and behold, a time difference of 1 second, creates a phase seperation of 90 degrees.

Answer 2

x1 = A sin ω t = A sin (2 pi f t)     equation for SHM with no phase

x1 =A sin (2 * pi * .25 t)  = A sin (.5 * pi * t)

x2 = A sin (.5  pi * (t - 1)) = A sin (.5 pi  t - pi/2)  second oscillator lags by 1 sec

So x2 is pi / 2 behind x1 in phase

Or x2 = A cos .5 pi t    since sin (Ф - pi/2) = cos Ф