All Problems Mechanical Oscillations
Problem 4.82
A bar of mass \(m=0.50\) kg lying on a horizontal plane with a friction coefficient \(k=0.10\) is attached to the wall by means of a horizontal non-deformed spring. The stiffness of the spring is equal to \(x=2.45 \mathrm{~N} / \mathrm{cm},\) its mass is negligible. The bar was displaced so that the spring was stretched by \(x_{0}=3.0 \mathrm{~cm},\) and then released. Find: (a) the period of oscillation of the bar; (b) the total number of oscillations that the bar performs until it stops completely.
4.82. (a) \(T=2 \pi \sqrt{m / x}=0.28 \mathrm{~s} ;\) (b) \(n=\left(x_{0}-\Delta\right) / 4 \Delta=3.5\) oscilla- tions, here \(\Delta=k m g / x\)