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  • The function of time representing a simple harmonic motion with period of  is Option: 1 <img alt="\sin (\omega t) + \cos (\omega

The function of time representing a simple harmonic motion with period of \frac{\pi}{\omega } is
Option: 1 \sin (\omega t) + \cos (\omega t)
Option: 2 3 \cos \left ( \frac{\pi}{4} -2 \omega t \right )
Option: 3 \cos (\omega t) + \cos (2 \omega t)+ \cos (3 \omega t)
Option: 4 \sin ^2 (\omega t)

Answers (1)

best_answer

\begin{array}{l} \text { Time period } T =\frac{2 \pi}{\omega^{\prime}} \\\\ \frac{\pi}{\omega}=\frac{2 \pi}{\omega^{\prime}} \\\\ \omega^{\prime}=2 \omega \rightarrow \text { Angular frequency of } SHM \end{array}

Option (4)
\begin{aligned} &\sin ^{2} \omega t =\frac{1}{2}\left(2 \sin ^{2} \omega t \right)=\frac{1}{2}(1-\cos 2 \omega t )\\ &\text { Angular frequency of }\left(\frac{1}{2}-\frac{1}{2} \cos 2 \omega t \right) \text { is } 2 \omega \end{aligned}
Option (2)
\begin{aligned} &\text { Angular frequency of SHM }\\ &3 \cos \left(\frac{\pi}{4}-2 \omega t\right) \text { is } 2 \omega . \end{aligned}
\text{ So option (2) \& (4) both have angular frequency $2 \omega$ but option (2) is direct answer.}

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Deependra Verma

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