All Problems

Mechanical Oscillations

Problem 4.15

Find the trajectory equation y(x)y(x) of a point if it moves according to the following laws: (a) x=asin⁡ωt,y=asin⁡2ωtx=a \sin \omega t, \quad y=a \sin 2 \omega t (b) x=asin⁡ωt,y=acos⁡2ωtx=a \sin \omega t, y=a \cos 2 \omega t. Plot these trajectories.

Reveal Answer
4.15. (a) y2=4x2(1−x2/a2)y^{2}=4 x^{2}\left(1-x^{2} / a^{2}\right) (b) y=a(1−2x2/a2).\quad y=a\left(1-2 x^{2} / a^{2}\right) . See Fig. 29.29 .
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