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Mechanical Oscillations

Problem 4.67

A point performs damped oscillations according to the law x=a0e−βtsin⁡ωt.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=0t=0 (b) the moments of time at which the point reaches the extreme positions.

Reveal Answer
 4.67. (a) a0 and a0ω;\begin{array}{lllll}\text { 4.67. (a) } & a_{0} \text { and } & a_{0} \omega ;\end{array} (b) tn=1ω(arctan⁡ωβ+nπ),t_{n}=\frac{1}{\omega}\left(\arctan \frac{\omega}{\beta}+n \pi\right), where n=0,1,2,…n=0,1,2, \ldots
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