For the shown spring–mass system, if the period of small oscillations about mean position is π√(nm/K), find n. Assume ideal conditions. K₁=2K and K₂=K.

Question

G1 Physics · Accepted Answer

Using the pulley displacement constraint, the restoring force on the mass corresponds to effective spring constant Kₑ=K/3. Hence T=2π√(m/Kₑ)=2π√(3m/K)=π√(12m/K). Comparing with π√(nm/K) gives n=12.