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In the figure given below, a block of mass M = 490g placed on a frictionless table is connected with two springs having same spring constant $(K = 2 N m^{- 1})$ . If the block is horizontally displaced through ' X ' m then the number of complete oscillations it will make in 14 $π$ seconds will be ____.

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answer is 20.

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Detailed Solution

The given case will have an effective spring constant of 2K.

We know, time period of a spring mass system is given by

$T = 2 π \sqrt{\frac{m}{k_{eff}}}$

$∴ T = 2 π \sqrt{\frac{m}{2 K}}$

$= 2 π \sqrt{\frac{0.49}{4}} = 2 π \times \frac{0.7}{2} n = \frac{14 π}{π \times 0.7} = 20$

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