Question asked by Filo student

$D=\sqrt{A^2+B^2}\text{ and }\varphi ={\tan }^{-1}\left(\frac{B}{A}\right)$ The great importance of periodic sine and cosine functions is due to a remarkable result proved by the French mathematician. Jean Baptiste Joseph Fourier (1768-1830): Any periodic function can be expressed as a superposition of sine and cosine functions of different time periods with suitable coefficients. Example 14.2 Which of the following functions of time represent (a) periodic and (b) non-periodic motion? Give the period for each case of periodic motion $[\omega$ is any positive constant].

1. $\sin \omega t+\cos \omega t$
2. $\sin \omega t+\cos 2\omega t+\sin 4\omega t$.
3. ${\mathrm{e}}^{-\mathrm{t}}$
4. $\log (\omega t)$

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Updated on: Mar 10, 2023