A particle connected to the end of a spring executes S.H.M. with period ' T 1 '. While the corresponding period for another spring is ' T 2 '. If the period of oscillation with

Question

A particle connected to the end of a spring executes S.H.M. with period ' T 1 ​ '. While the corresponding period for another spring is ' T 2 ​ '. If the period of oscillation with two springs in series is ' T ', then

TestHub · Accepted Answer

T 1 ​ = 2 π k 1 ​ m ​ ​ T 2 ​ = 2 π k 2 ​ m ​ ​ When the two springs are connected in series, the effective spring constant is given by T = 2 π k m ​ ​ ​ ∴ T 2 = 4 π 2 k m ​ = 4 π 2 m [ k 1 ​ 1 ​ + k 2 ​ 1 ​ ] = 4 π 2 k 1 ​ m ​ + 4 π 2 k 2 ​ m ​ = T 1 2 ​ + T 2 2 ​ ∴ T = T 1 2 ​ + T 2 2 ​ ​ ​

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