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In the arrangement shown in figure, pulleys are small and light and springs are ideal and  and  are the force constants of the springs. Calculate the period of small vertical oscillations of block of mass



Question ID - 153912 | SaraNextGen Top Answer

In the arrangement shown in figure, pulleys are small and light and springs are ideal and  and  are the force constants of the springs. Calculate the period of small vertical oscillations of block of mass

1 Answer
127 votes
Answer Key / Explanation : (2) -

(2)

In static equilibrium of block, tension in the string is exactly equal to its weight. Let a vertically downward force  be applied on the block to pull it downward. Equilibrium is again restored when tension in the string is increased by the same amount . Hence, total tension in the string becomes equal to .Strings are further elongated due to the extra tension . Due to this extra tension  in strings, tension in each spring increases by .Hence increases in elongation of springs is , respectively

According to geometry of the arrangement, downward displacement of the block from its equilibrium position is

If the block is released now, it starts to accelerate upwards due to extra tension  in the strings. It means restoring force on the block is equal to .From Eq.(i),

Restoring acceleration of block

Since acceleration of block is restoring and is directly proportional to displacement  the block performs SHM

Its period

After substitution the values we get

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