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Identify the function which represents a periodic motion

Option: 1
$\log _e\left ( \omega t \right )$

Option: 2
$\sin \omega t+\cos\omega t$

Option: 3
$e^{- \omega t}$

Option: 4
$e^{ \omega t}$

Answers (1)

best_answer

For periodic function

$f(t)= f(t+T)$

T - Time period

(1) For $f(t)=\log _e (\omega t)$

$f(t+T)=\log _e (\omega (t+T))$

$f(t)\neq f(t+T)$

(2) For $f(t) = \sin \omega t + \cos \omega t$

$f(t+T) = \sin (\omega (t+T) )+ \cos( \omega( t+T))$

$(\because \omega T = 2\pi )$

$f(t) = f(t+T)$

(3) $f(t)=e^{-\omega t}$

$f(t+T)=e^{-\omega( t+T)}$

$f(t)\neq f(t+T)$

(4) $f(t)=e^{\omega t}$

$f(t+T)=e^{\omega( t+T)}$

$f(t)\neq f(t+T)$

So $f(t) = \sin \omega t + \cos \omega t$ is the periodic function

Posted by

Suraj Bhandari

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