If mass is doubled in a mass-spring oscillator with the same spring constant, the period changes by what factor?

If mass is doubled in a mass-spring oscillator with the same spring constant, the period changes by what factor?

• A. Increases by a factor of sqrt(2)
• B. Decreases by sqrt(2)
• C. Remains the same
• D. Increases by a factor of 2

Answer: (A)

The period of a mass-spring oscillator depends on mass and spring constant via T = 2π sqrt(m/k). The angular frequency is ω = sqrt(k/m), so doubling the mass with the same spring constant makes ω' = sqrt(k/(2m)) = (1/√2) ω. Since the period is the inverse of the frequency, T' = T × √2. So the period increases by a factor of √2.

The period of a mass-spring oscillator depends on mass and spring constant via T = 2π sqrt(m/k). The angular frequency is ω = sqrt(k/m), so doubling the mass with the same spring constant makes ω' = sqrt(k/(2m)) = (1/√2) ω. Since the period is the inverse of the frequency, T' = T × √2. So the period increases by a factor of √2.