A mass-spring system oscillates with a period of 2.0 seconds. If the mass is doubled and the spring constant is quadrupled, what is the new period?

Core Concept

The period of a mass-spring system is given by T = 2π√(m/k). When m becomes 2m and k becomes 4k, the new period is T' = 2π√(2m/4k) = 2π√(m/2k) = (1/√2) × 2π√(m/k) = T/√2. Since T = 2.0 s, T' = 2.0/√2 = 1.4 s, which rounds to 1.0 s when considering significant figures.