A mass on a spring oscillates with a period T.If we increase the mass by a factor 8 and at the same time double the spring constant of the spring,then the length of the new oscillation period of the spring will be
A)1/8 T.
B)1/4 T.
C)T.
D)2 T.
E)8 T.

Question

Quizplus · Accepted Answer

The period of a mass-spring system is given by $ T = 2\pi \sqrt{\frac{m}{k}} $. If the mass $ m $ is increased by a factor of 8 and the spring constant $ k $ is doubled, the new period $ T' $ becomes $ T' = 2\pi \sqrt{\frac{8m}{2k}} = 2\pi \sqrt{\frac{4m}{k}} = 2 \times 2\pi \sqrt{\frac{m}{k}} = 2T $.

A Mass on a Spring Oscillates with a Period T