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  4. A particle, doing simple harmonic motion, at a distance 3 cm from mean position has acceleration 12 cm / s 2. What is its time period?

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Q. A particle, doing simple harmonic motion, at a distance $3\, cm$ from mean position has acceleration $12\, cm / s ^{2}$. What is its time period?

ManipalManipal 2020

Solution:

The time period of a particle executing SHM is given as
$T=2 \pi \sqrt{\frac{x}{a}}=2 \pi \sqrt{\frac{\text { Displacement }}{\text { Acceleration }}}$ $=2 \pi \sqrt{\frac{3 \times 10^{-2}}{12 \times 10^{-2}}}$
$=2 \pi \times \frac{1}{2}$
$=\pi=3.14\, s$