All Problems Mechanical Oscillations
Problem 4.67
A point performs damped oscillations according to the law \(x=a_{0} \mathrm{e}^{-\beta t} \sin \omega t .\) Find: (a) the oscillation amplitude and the velocity of the point at the moment \(t=0\) (b) the moments of time at which the point reaches the extreme positions.
\(\begin{array}{lllll}\text { 4.67. (a) } & a_{0} \text { and } & a_{0} \omega ;\end{array}\) (b) \(t_{n}=\frac{1}{\omega}\left(\arctan \frac{\omega}{\beta}+n \pi\right),\) where \(n=0,1,2, \ldots\)