Final answer:
To find the Fourier series for a function with period T, one must calculate the Fourier coefficients, which involves using the relationship between the period T and the frequency f, where f = 1/T.
Step-by-step explanation:
The student has asked how to find the Fourier series for a function f(x) that is periodic with period T. In physics and mathematics, the Fourier series is a way to represent a periodic function as the sum of simple sine and cosine waves. For a function with period T, the frequency, f, is inversely related to T, and is given by f = 1/T. This relationship is crucial when working with oscillations and waves in both mathematics and physics. Using this relationship, one can derive the Fourier coefficients that compose the series which approximate the given function.
For simple harmonic motion, the period T and frequency f are defined independent of the amplitude and relate to the properties of the system, such as mass and torsion constant. To find the Fourier series, we generally compute the Fourier coefficients, which requires an understanding of integral and trigonometric functions, and typically involves calculating the integrals of the product of the function and sine and cosine functions over one period of the function.