In a mass-spring system, if the mass is doubled while the spring constant remains fixed, the period will

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Multiple Choice

In a mass-spring system, if the mass is doubled while the spring constant remains fixed, the period will

Explanation:
The period of a mass-spring oscillator scales with the square root of the mass, T ∝ sqrt(m/k). With the spring constant fixed, doubling the mass gives T' = 2π sqrt((2m)/k) = sqrt(2) times the original period. Since sqrt(2) ≈ 1.414, the period increases by about 41%. (For reference, the frequency would decrease by about 29%, since f ∝ 1/√m, but the question asks about the period.)

The period of a mass-spring oscillator scales with the square root of the mass, T ∝ sqrt(m/k). With the spring constant fixed, doubling the mass gives T' = 2π sqrt((2m)/k) = sqrt(2) times the original period. Since sqrt(2) ≈ 1.414, the period increases by about 41%.

(For reference, the frequency would decrease by about 29%, since f ∝ 1/√m, but the question asks about the period.)

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