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Q.

As per given figures, two springs of spring constants K and 2K are connected to mass ‘m’. If the period of oscillation in fig (a) is 3s, then the period of oscillation in fig. (b) will be $\sqrt{x} s .$ The value of ‘x’ is …..

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Detailed Solution

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For fig (a) :

$K_{e q} = \frac{K \times 2 K}{K + 2 K} = \frac{2 K}{3}$

$T = 2 π \sqrt{\frac{m}{K_{e q}}} = 2 π \sqrt{\frac{m}{2 K / 3}} = 2 π \sqrt{\frac{3 m}{2 K}}$

For fig. (b) :

$\frac{T}{T} = \sqrt{\frac{m \times 2 K}{3 K \times 3 m}} = \frac{\sqrt{2}}{3}$

$T' = \sqrt{2}$

$x = 2$

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As per given figures, two springs of spring constants K and 2K are connected to mass ‘m’. If the period of oscillation in fig (a) is 3s, then the period of oscillation in fig. (b) will be x s. The value of ‘x’ is …..