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Two ideal springs of spring constants K each are attached to a block of mass m and 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

When mass m is displaced to right (small distance x)

$F = F_{1} + F_{2} = - 2 k x$

$a = \frac{- 2 k x}{m}$

Comparing with a = $- w^{2} x$

$w = \sqrt{\frac{2 k}{m}}, T = \frac{2 π}{w}$ $T = 2 π \sqrt{\frac{m}{2 K}}$

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