A mass m is attached to a vertical spring with a force constant k, it oscillates with a period T. If the spring is cut to one third of its original length and the same mass is attached to it, the new period of oscillation will be
A) less than T.
B) greater than T.
C) equal to T.
D) It could be greater or less than T, depending on how you cut the spring.

Question

Quizplus · Accepted Answer

The period of oscillation for a mass-spring system is given by $ T = 2\pi \sqrt{\frac{m}{k}} $. When the spring is cut to one third of its original length, the spring constant $ k $ becomes three times larger (since $ k \propto \frac{1}{L} $). Therefore, the new period $ T' = 2\pi \sqrt{\frac{m}{3k}} $ is less than the original period $ T $.

A Mass M Is Attached to a Vertical Spring with a Force