Two equal masses hung from two massless springs of spring constants k 1 and k 2 . They have equal maximum velocity when executing simple harmonic motion. The ratio of their amplitudes is

Question

Two equal masses hung from two massless springs of spring constants k 1 and k 2 . They have equal maximum velocity when executing simple harmonic motion. The ratio of their amplitudes is, k 1 k 2 1 2, k 1 k 2, k 2 k 1, k 2 k 1 1 2

MARKS App · Accepted Answer

As the masses are executing S H M the velocity, v = a ω ∵ v 1 = v 2 (given) ∴ a 1 ω 1 = a 2 ω 2 a 1 a 2 = ω 2 ω 1 .....(i) We know that the time period, T = 2 π m k T 2 π = m k ⇒ 1 ω = m k ⇒ ω = k m ⇒ ω ∝ k .....(ii) From Equations (i) and (ii), we get a 1 a 2 = k 2 k 1

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