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Two identical springs are connected to mass m as shown (k = spring constant). If the period of the configuration (i) is 2 s, the period of the configuration (ii) is |
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Answer» `SQRT(2s)` Therefore, their effective spring constant is, `k_(s) =((K)(k))/(k+k) = k/2`  `therefore` Time period of oscillation, `T_(s) = 2pi sqrt(m/k_(s))`........(i) In figure, (ii) the two springs are connected in parallel. Therefore, their effective spring constant is `k_(p) = k + k = 2k` `therefore` time period of oscillation, `T_(P) = 2pi sqrt(m/k_(p))`...........(ii)  Divide (i) by (ii), we get `T_(s)/T_(p) = sqrt(k_(p)/k_(s)) = sqrt((2k)/(k//2)) =2` or `T_(p) = T_(s)/2 =(2s)/2 = 1s` |
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