The upper end of the spring is fixed and a mass ' m ' is attached to its lower end. When mass is slightly pulled down and released, it oscillates with time period 3 second. If mass ' m

Question

The upper end of the spring is fixed and a mass ' m ' is attached to its lower end. When mass is slightly pulled down and released, it oscillates with time period 3 second. If mass ' m ' is increased by 1 kg , the time period becomes 5 second. The value of ' m ' is (mass of spring is negligible)

TestHub · Accepted Answer

The formula for the time period of a spring mass system is T = 2 π k m ​ ​ For mass m + 1 , T ′ = 2 π k m + 1 ​ ​ Taking the ratio, ​ T ′ T ​ = 2 π k m + 1 ​ ​ 2 π k m ​ ​ ​ T T ​ = m + 1 m ​ ​ 5 3 ​ = m + 1 m ​ ​ 25 9 ​ = m + 1 m ​ ∴ 9 m + 9 = 25 m ∴ 16 m = 9 ∴ m = 16 9 ​ kg ​

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