Math Help Forum - View Single Post

topsquark · #2 May 21st, 2008, 03:34 PM

Quote:

Originally Posted by delpin

Physical potential Period 23 days
Emotional potential period 28 days
Intellectual potential period 33 days

If the equation determining each of your "potentials" is of the form

P(t)= 50 sin (at) + 50 where t is days and a is a constant specific to each of your potentials and P(t) is your potential after t days expressed as a percentage

How to find the value of a for each potential

And how to determine when the three "potentials" are each at their peak of 100%

when t=0 all potentials start at 50%

Any help always appreciated

To find a: Call the period of the cycle T. Then we know that one cycle corresponds to a time T. Thus
$2 \pi = a T$

$a = \frac{2 \pi}{T}$

Each potential is at its peak when $sin(at) = 1$ . So when
$at = \frac{\pi}{2}$

$t = \frac{\pi}{2a}$
or, if you insert the value of a from the first part:
$t = \frac{\pi}{2 \frac{2 \pi}{T}} = \frac{T}{4}$

-Dan