All Problems Mechanical Oscillations
Problem 4.2
A point moves along the \(x\) axis according to the law \(x\) \(=a \sin ^{2}(\omega t-\pi / 4) .\) Find: (a) the amplitude and period of oscillations; draw the plot \(x(t)\) (b) the velocity projection \(v_{x}\) as a function of the coordinate \(x\); draw the plot \(v_{x}(x)\).
4.2. (a) The amplitude is equal to \(a / 2,\) and the period is \(T=\) \(=\pi / \omega\) see Fig. \(28 a\) (b) \(v_{x}^{2}=4 \omega^{2} x(a-x),\) see Fig. \(28 b\)