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  4. The maximum speed of a particle executing SHM is 10 m / s and maximum acceleration is 31.4 m / s 2 . Its periodic time is

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Q. The maximum speed of a particle executing SHM is $10\, m\, / s$ and maximum acceleration is $31.4 \,m / \,s ^{2} .$ Its periodic time is

Oscillations

Solution:

Maximum speed, $v_{m}=\omega A$
Maximum acceleration, $a_{m}=\omega^{2} A$
$\therefore \,\,\,\,\,\frac{a_{m}}{v_{m}}=\omega=\frac{2 \pi}{T} \,\,\,\,\,$ or $\,\,\,\,\,\frac{31.4}{10}=\frac{2 \times 3.14}{T}$ or $T=2 s$