Which of the following functions has a period | vedclass

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(C) function $y = f(t)$ is periodic with period $T$ if $f(t + T) = f(t)$.For option $(a)$,the terms have frequencies $2\pi, 3\pi, 5\pi$. The periods a

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$y = \sin t + \cos 2t$

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(C) function $y = f(t)$ is periodic with period $T$ if $f(t + T) = f(t)$.For option $(a)$,the terms have frequencies $2\pi, 3\pi, 5\pi$. The periods are $T_1 = \frac{2\pi}{2\pi} = 1$,$T_2 = \frac{2\pi}{3\pi} = \frac{2}{3}$,$T_3 = \frac{2\pi}{5\pi} = \frac{2}{5}$. The $LCM$ of $(1, \frac{2}{3}, \frac{2}{5})$ is $2$.For option $(b)$,the periods are $T_1 = \frac{2\pi}{\pi/3} = 6$ and $T_2 = \frac{2\pi}{\pi/4} = 8$. The $LCM$ of $(6, 8)$ is $24$.For option $(c)$,the period of $\sin t$ is $2\pi$ and the period of $\cos 2t$ is $\frac{2\pi}{2} = \pi$. The $LCM$ of $(2\pi, \pi)$ is $2\pi$. Thus,the function $y = \sin t + \cos 2t$ has a period of $2\pi$.

Which of the following functions has a period of $2\pi$?

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