The time period of oscillations of a block attached to a spring is t 1 . When the spring is replaced by another spring, the time period of the block is t 2 . If both the springs are connected in serie

Question

The time period of oscillations of a block attached to a spring is t 1 . When the spring is replaced by another spring, the time period of the block is t 2 . If both the springs are connected in series and the block is made to oscillate using the combination, then the time period of the block is

TestHub · Accepted Answer

When springs are in series, k = k 1 k 2 k 1 + k 2 For first spring, t 1 = 2 π m k 1 For Second spring, t 2 = 2 π m k 2 ∴ t 1 2 + t 2 2 = 4 π 2 m k 1 + 4 π 2 m k 2 = 4 π 2 m k 1 + k 2 k 1 k 2 or t 1 2 + t 2 2 = 2 π m k 1 + k 2 k 1 k 2 2 or t 1 2 + t 2 2 = T 2 .

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