All Problems

Mechanical Oscillations

Problem 4.2

A point moves along the xx axis according to the law xx =asin⁡2(ωt−π/4).=a \sin ^{2}(\omega t-\pi / 4) . Find: (a) the amplitude and period of oscillations; draw the plot x(t)x(t) (b) the velocity projection vxv_{x} as a function of the coordinate xx; draw the plot vx(x)v_{x}(x).

Reveal Answer
4.2. (a) The amplitude is equal to a/2,a / 2, and the period is T=T= =π/ω=\pi / \omega see Fig. 28a28 a (b) vx2=4ω2x(a−x),v_{x}^{2}=4 \omega^{2} x(a-x), see Fig. 28b28 b
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