A body of mass m is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass m is slightly pulled down and released, it oscillates with a time period of 3 s. When the mass m is increased by 1 kg, the time period of oscillations becomes 5 s. The v…

Question

A body of mass m is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass m is slightly pulled down and released, it oscillates with a time period of 3 s. When the mass m is increased by 1 kg, the time period of oscillations becomes 5 s. The value of m in kg is

Accepted Answer

(4) 9/(16). Given: T₁=3 s with mass m, and T₂=5 s with mass m+1. Idea: for a spring T=2π√m/k, so T²∝ m and the unknown k cancels in the ratio. (T₂²)/(T₁²)=(m+1)/m (25)/9=(m+1)/m 25m=9m+9 16m=9, so m=9/(16) kg

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