Q113 / 180 · AIIMS 2005 · Physics
Which of the following functions represents a simple harmonic oscillation?
- Correct answerA$\sin \omega t-\cos \omega t$
- B$\sin ^2 \omega t$
- C$\sin \omega t+\sin 2 \omega t$
- D$\sin \omega t-\sin 2 \omega t$
Solution
$y=\sin \omega t-\cos \omega t$
$$
\begin{aligned}
\frac{d y}{d t} & =\omega \cos \omega t+\omega \sin \omega t \\
\frac{d y}{d t} & =-\omega^2 \sin \omega t+\omega^2 \cos \omega t \\
& =-\omega^2(\sin \omega t-\cos \omega t) . \\
a & =-\omega^2 y . \quad \therefore a \propto-y .
\end{aligned}
$$
which is the condition of simple harmonic motion.
Hence, the correct answer is option: 'A'.