Sum of sinosoids that can be a Fourier Series expansion

[Chris Y]

Homework Statement

I was given a problem with a list of sums of sinusoidal signals, such as
Example that I made up: x(t)=cos(t)+5sin(5*t). The problem asks if a given expression could be a Fourier expansion.

Homework Equations

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The Attempt at a Solution

My guess is that it has something to do with 5 being an integer multiple of 1.

 

[LCKurtz]

Homework Statement

I was given a problem with a list of sums of sinusoidal signals, such as
Example that I made up: x(t)=cos(t)+5sin(5*t). The problem asks if a given expression could be a Fourier expansion.

Homework Equations

[/B]

The Attempt at a Solution

My guess is that it has something to do with 5 being an integer multiple of 1.

Can you write your sum as$$
\cos t + 5\sin(5t) = a_0 + \sum_{n=1}^\infty \left ( a_n\cos(\frac {n\pi t} p) + b_n\sin(\frac {n\pi t} p)\right )$$
by choosing certain values for the $a_n,~b_n,~p$? Hint: lots of them can be $0$.