Two ideal springs of force constants k₁ and k₂ are connected in series and a mass m is attached to the free end on a smooth horizontal surface. Which expression gives the time period of small oscillations?
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Question

Two ideal springs of force constants k₁ and k₂ are connected in series and a mass m is attached to the free end on a smooth horizontal surface. Which expression gives the time period of small oscillations?

Options

G1 Physics · Accepted Answer

For springs in series, 1/kₑ = 1/k₁+1/k₂. Hence, kₑ = k₁k₂/(k₁+k₂). The time period is T = 2π√[m/kₑ] = 2π√[m(k₁+k₂)/(k₁k₂)]. Correct option: A.