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Mechanical Oscillations

Problem 4.7

A particle moves along the \(x\) axis according to the law \(x\) \(=a \cos \omega t .\) Find the distance that the particle covers during the time interval from \(t=0\) to \(t\).

Reveal Answer
 4.7. s={a[n+1−cos⁡(ωt−nπ/2)],n is even a[n+sin⁡(ωt−nπ/2)],n is odd.  Here n is a whole number of the ratio 2ωt/π\begin{aligned} &\text { 4.7. } s=\left\{\begin{array}{l} a[n+1-\cos (\omega t-n \pi / 2)], n \text { is even } \\ a[n+\sin (\omega t-n \pi / 2)], n \text { is odd. } \end{array}\right.\\ &\text { Here } n \text { is a whole number of the ratio } 2 \omega t / \pi \end{aligned}
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