The time period of simple harmonic motion of mass M in the given figure is π√(αM/5K), where the value of α i $s _______.$

Question

The time period of simple harmonic motion of mass M in the given figure is π√(αM/5K), where the value of α i s _______.

G1 Physics · Accepted Answer

Image The two upper right springs of spring constant K are in parallel: K + K = 2K This 2K combination is in series with the lower spring K: K' = (2K × K)/(2K + K) = 2K/3 This branch is in parallel with the left spring K: Kₑq = K + 2K/3 = 5K/3 Angular frequency: ω = √(Kₑq/M) = √(5K/3M) Time period: T = 2π/ω = 2π√(3M/5K) = π√(12M/5K) Comparing with: T = π√(αM/5K) we get, α = 12