A particle at the end of a spring executes S.H.M. with a period t₁. While the corresponding period for another spring is t₂. If the period of oscillation with the two springs in series is T then (a) T⁻¹ = t₁⁻¹ + t₂⁻¹ (b) T² = t₁² + t₂² (c) T = t₁ + t₂ (d) T⁻² = t₁⁻² + t₂⁻²

Answer: (b). Series: 1/k = 1/k₁ + 1/k₂. T² ∝ 1/k, so T² = t₁² + t₂². So the answer is (b).

A particle at the end of a spring executes S.H.M. with a period t₁… | JEE Main 2004 (AIEEE)

Q93JEE Main 2004 · AIEEEMedium

Spring Systems

A particle at the end of a spring executes $\text{S.H.M.}$ 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

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Answer: (b)

Series: $\frac{1}{k} = \frac{1}{k_1} + \frac{1}{k_2}$ .
$T^2 \propto \frac{1}{k}$ , so $T^2 = t_1^2 + t_2^2$ .
So the answer is (b).

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