The time period of simple harmonic motion of mass M in the given figure is π α M 5 K , where the value of α is _______.

Step-by-step solution

For series combination of the spring, equivalent spring constant is given by, 1 k e q = 1 k 1 + 1 k 2 . Therefore, for combined system net spring constant k e q = 2 k × k 2 k + k + k = 5 k 3 Angular frequency of oscillation ω = k e q m ⇒ ω = 5 k 3 m Period of oscillation τ = 2 π ω = 2 π 3 m 5 k = π 12 m 5 k Therefore, α = 12 .