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Q.

When a block is suspended by a spring and allowed to oscillate vertically, its time period is 1 sec. When the same block is suspended by another spring, its time period is found to be 2 sec. Now the springs are connected end to end to form a longer spring and the same block is suspended from the combination of springs, the new time period of small vertical oscillations of the block is

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answer is 2.

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Detailed Solution

T1=2πmk1⇒k1=4π2mT12;similarly k2=4π2mT22For series combination of springs, 1ke=1k1+1k2⇒Te24π2m=T124π2m+T224π2m∴Te=T12+T22=12+22sec=5sec
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