MHT CET202122 Sep 2021Evening ShiftPhysicsOscillationsActual
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 ' T₂ '. If the period of oscillation with two springs in series is ' T ', then
Options
- AT = T ₁^2+ T ₂^2
- BT = T ₂^2- T ₁^2
- CT = T ₁+ T ₂
- DT = T ₁- T ₂
Correct answer
A. T = T ₁^2+ T ₂^2
Step-by-step solution
T ₁=2 m k ₁ ~T ₂=2 m k ₂ When the two springs are connected in series, the effective spring constant is given by T =2 m k aligned & T ^2=4 ^2 m k =4 ^2 ~m [ 1 k ₁ + 1 k ₂ ]=4 ^2 m k ₁ +4 ^2 m k ₂ & = T ₁^2+ T ₂^2 & T = T ₁^2+ T ₂^2 aligned