Question
Write the differential equation and two difference of time period in linear and angular simple harmonic motion.
✓
Answer
Linear simple harmonic motion differential equation of motion
$
\begin{aligned}
\frac{d^2 y}{dt^2}+\omega^2 y & =0 \\
\omega & =\sqrt{\frac{k}{m}}
\end{aligned}
$
Period of motion $T=2 \pi \sqrt{\frac{m}{ k }}$
Angular simple harmonic motion differential equation of motion
$\frac{ d ^2 \theta}{ dt ^2}+\omega^2 \theta=0$
$\omega=\sqrt{\frac{ C }{ I }}$
Time period of motion $T=2 \pi \sqrt{\frac{ I }{ C }}$
$
\begin{aligned}
\frac{d^2 y}{dt^2}+\omega^2 y & =0 \\
\omega & =\sqrt{\frac{k}{m}}
\end{aligned}
$
Period of motion $T=2 \pi \sqrt{\frac{m}{ k }}$
Angular simple harmonic motion differential equation of motion
$\frac{ d ^2 \theta}{ dt ^2}+\omega^2 \theta=0$
$\omega=\sqrt{\frac{ C }{ I }}$
Time period of motion $T=2 \pi \sqrt{\frac{ I }{ C }}$
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