A mass m is suspended from a spring of force constant k and just...

A mass

\mathrm{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 A mass m is suspended from a spring of force constant k and just touches another identical spring fixed to the floor as

A mass m is suspended from a spring of force constant k and just touches another identical spring fixed to the floor as

Options

A $2 \pi \sqrt{\frac{\mathrm{m}}{\mathrm{k}}}$
B $\pi \sqrt{\frac{\mathrm{m}}{\mathrm{k}}}+\pi \sqrt{\frac{\mathrm{m}}{\mathrm{k} / 2}}$
C $\pi \sqrt{\frac{\mathrm{m}}{3 \mathrm{k} / 2}}$
D $\pi \sqrt{\frac{\mathrm{m}}{\mathrm{k}}}+\pi \sqrt{\frac{\mathrm{m}}{2 \mathrm{k}}}$ .

Correct answer

D. $\pi \sqrt{\frac{\mathrm{m}}{\mathrm{k}}}+\pi \sqrt{\frac{\mathrm{m}}{2 \mathrm{k}}}$ .

Step-by-step solution

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

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

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