A mass $m$ is suspended from a spring of force constant $k$ and just touches another identical spring fixed to the floor as shown in the figure. The time period of small oscillations is 
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(d)

When the spring undergoes displacement in the downward direction it completes one half oscillation while it completes another half oscillation in the upward direction. The total time period is:

$T =\pi \sqrt{\frac{ m }{ k }}+\pi \sqrt{\frac{ m }{2 k }}$

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