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  4. A spring block system in horizontal oscillation has a time-period T. Now the spring is cut into four equal parts and the block is re-connected with one of the parts. The new time period of vertical oscillation will be

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Q. A spring block system in horizontal oscillation has a time-period $T$. Now the spring is cut into four equal parts and the block is re-connected with one of the parts. The new time period of vertical oscillation will be

Oscillations

Solution:

When spring is cut into $4$ parts.
The spring constant of each part will become $4 \,k$.
$T_{2}=2 \pi \sqrt{\frac{m}{4 k}} $
$T_{2}=\frac{T}{2}$