Question

The period of oscillation of a body of mass m₁ suspended from a light spring is T. When a body of mass m₂ is tied to the first body and the system is made to oscillate, the period is 2T. Compare the masses m₁ and m₂

Answer 1

For mass m₁, period is T

∴ T = 2π\(\sqrt{\frac{m_1}{k}}\)

For mass m₂, period is 2T

∴ 2T = 2π\(\sqrt{\frac{m_1+m_2}{k}}\)

∴ 2T/T = 2 = \(\sqrt{\frac{m_1+m_2}{m_1}}\)

∴ \(\frac{m_1+m_2}{m_1}\) = 4

∴ \(\frac{m_2}{m_1}\) = 3

∴ \(\frac{m_1}{m_2}\) = \(\frac{1}{3}\)