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Two ideal springs of spring constants K each are attached to a block of mass m to fixed supports as shown. The time period of oscillation is

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$2 π \sqrt{\frac{m}{K}}$

$2 π \sqrt{\frac{2 m}{K}}$

$π \sqrt{\frac{m}{2 K}}$

$2 π \sqrt{\frac{m}{2 K}}$

answer is B.

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Detailed Solution

$F = F_{1} + F_{2} = - 2 K x$
$a = - \frac{2 K x}{m},$ comparing with $a = - ω^{2} k$
$ω = \sqrt{\frac{2 k}{m}}, T = 2 π \sqrt{\frac{m}{2 k}}$

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