A particle at the end of a spring executes simple harmonic motion with a period t 1 , while the corresponding period for another spring is t 2 . If the period of oscillation with the two springs in series is T , then -

Question

A particle at the end of a spring executes simple harmonic motion with a period t 1 , while the corresponding period for another spring is t 2 . If the period of oscillation with the two springs in series is T , then -, T = t 1 + t 2, T 2 = t 1 2 + t 2 2, T - 1 = t 1 - 1 + t 2 - 1, T - 2 = t 1 - 2 + t 2 - 2

MARKS App · Accepted Answer

t 1 = 2 π m k 1 … . i , t 2 = 2 π m k 2 … . i i when springs are in series then T = 2 π m k 1 k 2 k 1 + k 2 = 2 π m k 1 + k 2 k 1 k 2 squaring and adding (i) and (ii) we get 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 = T 2

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