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Your solution is correct. Obviously, any periodic function with period $T$ is also periodic with period $kT$, $k\in\mathbb{Z}^+$. In the given example, the smallest possible period is $T=1/5$, which is equivalent to $\omega_0=10\pi$. There is no obvious reason why one should choose $T^\prime=kT$ and $\omega_0^{\prime}=\omega_0/k$, with $k>1$. Nevertheless,...


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Fourier series is used to obtain any function using the weighted summation of sinusoidal functions. The above sinusoidal function is also obtained using weighted sums of different sinusoidal frequencies with the fundamental frequency being ω0=2π and its harmonics. You can find a lot of detail about Fourier series and how its coefficients are calculated here: ...


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