All Problems Mechanical Oscillations
Problem 4.15
Find the trajectory equation \(y(x)\) of a point if it moves according to the following laws: (a) \(x=a \sin \omega t, \quad y=a \sin 2 \omega t\) (b) \(x=a \sin \omega t, y=a \cos 2 \omega t\). Plot these trajectories.
4.15. (a) \(y^{2}=4 x^{2}\left(1-x^{2} / a^{2}\right)\) (b) \(\quad y=a\left(1-2 x^{2} / a^{2}\right) .\) See Fig. \(29 .\)