Two identical springs, each of spring constant k, are used separately and then in series with the same mass M. If Tₐ is the period with one spring and Tᵦ is the period with the series combination, Tᵦ/Tₐ = √x. Find x.

Question

G1 Physics · Accepted Answer

With one spring, kₑ=k, so Tₐ=2π√(M/k). With two identical springs in series, kₑ=k/2, so Tᵦ=2π√(2M/k)=√2 Tₐ. Therefore Tᵦ/Tₐ=√2=√x, hence x=2.