All Problems

Mechanical Oscillations

Problem 4.23

A non-deformed spring whose ends are fixed has a stiffness \(x=13 \mathrm{~N} / \mathrm{m} .\) A small body of mass \(m=25 \mathrm{~g}\) is attached at the point removed from one of the ends by \(\eta=1 / 3\) of the spring's length. Neglecting the mass of the spring, find the period of small longitudinal oscillations of the body. The force of gravity is assumed to be absent.

Reveal Answer
T=2πη(1η)m/x=0.13 sT=2 \pi \sqrt{\eta(1-\eta) m / x}=0.13 \mathrm{~s}