All Problems

Mechanical Oscillations

Problem 4.1

A point oscillates along the \(x\) axis according to the law \(x\) \(=a \cos (\omega t-\pi / 4) .\) Draw the approximate plots (a) of displacement \(x\), velocity projection \(v_{x}\), and acceleration projection \(w_{x}\) as functions of time \(t\) (b) velocity projection \(v_{x}\) and acceleration projection \(w_{x}\) as functions of the coordinate \(x\).

Reveal Answer
(a) See Fig. 27; (b) \(\left(v_{x} / a \omega\right)^{2}+(x / a)^{2}=1\) and \(w_{x}=-\omega^{2} x\).