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The equation of motion of a particle in S.H.M is $\large a + 16{\pi ^2}x\, = \,0$ . In the equation ‘a’ is the linear acceleration (in m/sec²) of the particle at a displacement ‘x’ in meter. The time period of S H M in seconds is

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$\frac{1}{4}$

$\frac{1}{2}$

answer is B.

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Detailed Solution

$\large a + 16{\pi ^2}x\, = \,0$

But S.H.M equation is $\large a\, = \, - {\omega ^2}x\, \Rightarrow \,{\omega ^2}\, = \,16{\pi ^2}$

$\large \Rightarrow \,w\, = \,4\pi \, \Rightarrow \,\frac{{2\pi }}{T}\, = \,4\pi \, \Rightarrow \,T\, = \,\frac{2}{4}\, = \,\frac{1}{2}\sec$

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