- #1
Rick66
- 6
- 0
Hello everybody,
I'm new to this forum so thanks for having me.
I'm trying to find the times when the extrema occur for a periodic wave f(t) equal to the sum of three sine waves.
Given
f(t) = sin(2∏at) + sin(2∏bt) +sin(2∏ct)
where a, b and c are whole numbers in lowest form (i.e. the wave has a frequency of 1), the first derivative test for extrema gives
f'(t) = 2∏acos(2∏at) + 2∏bcos(2∏bt) +2∏ccos(2∏ct) = 0.
Solving this for t would produce the times at which the extremas in f(t) occur. Since the wave is periodic, we can restrict the domain to 0 ≤ t ≤ 1.
I've tried solving this using Euler substitutes, trig ID's, inverse trig functions, manual calculations of real examples etc but just can't see my way to a solution. This problem is really holding me up so any help would be greatly appreciated.
Thanks
Rick66
I'm new to this forum so thanks for having me.
I'm trying to find the times when the extrema occur for a periodic wave f(t) equal to the sum of three sine waves.
Given
f(t) = sin(2∏at) + sin(2∏bt) +sin(2∏ct)
where a, b and c are whole numbers in lowest form (i.e. the wave has a frequency of 1), the first derivative test for extrema gives
f'(t) = 2∏acos(2∏at) + 2∏bcos(2∏bt) +2∏ccos(2∏ct) = 0.
Solving this for t would produce the times at which the extremas in f(t) occur. Since the wave is periodic, we can restrict the domain to 0 ≤ t ≤ 1.
I've tried solving this using Euler substitutes, trig ID's, inverse trig functions, manual calculations of real examples etc but just can't see my way to a solution. This problem is really holding me up so any help would be greatly appreciated.
Thanks
Rick66