cos(ax^2+b+T)=cos(ax^2+b)
Find T.
Edit:
Rough mistake!
Thank you @topsquark!
Hi all,
Hope some here can help me with this math problem.
Given,
y1 = ax^2 + b.
y2 = cos (y1).
where a and b are constants. Is y2 periodic with respect to x.? Visually using example, the graph, seems to be periodic. How do u find the exact period of such a function?
Thanks in advance.
regards,
cybershakith
Okay. So the function is not periodic.
But let's take an example,
y = Cos (2*PI*ax^2 + 2*PI*b)
where is a =0.01277777778 and b = 255.5555556;
From plotting this graph, it seems like the y values are peridoc over x = 900.
So how does it happen?
for x =0;
y = Cos (2*PI*ax^2 + 2*PI*b) = Cos 2*PI * 255.5555556;
for x = 900;
y = Cos (2*PI*ax^2 + 2*PI*b) = Cos 2*PI*( 255.5555556 + 0.01277777778*900^2 ) = Cos 2*PI*(10605.5555556);
for x =11;
y = Cos (2*PI*ax^2 + 2*PI*b) = Cos 2*PI*( 255.5555556 + 0.01277777778*11^2 ) = Cos 2*PI*(257.10166671138);
for x = 911;
y = Cos (2*PI*ax^2 + 2*PI*b) = Cos 2*PI*( 255.5555556 + 0.01277777778*911^2 ) = Cos 2*PI*(10860.10166855538); //slight difference due to lack of precision.
This is true for all x, it seems.
this is because fractional part of ax^2 and a(x+T)^2 terms are the same.
So is it periodic?