If the mass in a mass-spring system is doubled with the same spring constant, how does the angular frequency ω change?

If the mass in a mass-spring system is doubled with the same spring constant, how does the angular frequency ω change?

• A. It decreases by a factor of √2
• B. It increases by √2
• C. It remains the same
• D. It doubles

Answer: (A)

The angular frequency of a mass-spring system depends on the spring constant and the mass as ω = sqrt(k/m). If the mass is doubled, you get ω' = sqrt(k/(2m)) = (1/√2) sqrt(k/m) = ω/√2. So the frequency decreases by a factor of √2 when the mass doubles. The other options would imply the wrong dependence on mass: increasing, staying the same, or doubling don’t match the ω ∝ 1/√m relationship.

The angular frequency of a mass-spring system depends on the spring constant and the mass as ω = sqrt(k/m). If the mass is doubled, you get ω' = sqrt(k/(2m)) = (1/√2) sqrt(k/m) = ω/√2. So the frequency decreases by a factor of √2 when the mass doubles. The other options would imply the wrong dependence on mass: increasing, staying the same, or doubling don’t match the ω ∝ 1/√m relationship.