The equation motion of a particle in S.H.M is a + 16π² 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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$\frac{1}{2}$

$\frac{1}{4}$

answer is B.

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Detailed Solution

$a + 16 π^{2} x = 0$
But S.H.M equation is $a = - ω^{2} x \Rightarrow ω^{2} = 16 π^{2}$
$\Rightarrow w = 4 π \Rightarrow \frac{2 π}{T} = 4 π \Rightarrow T = \frac{2}{4} = \frac{1}{2} \sec$

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