Question

A particle moves in the x-y plane according to the scheme x = -8 sin m and y = -2 cos 2m, where t is time. Find the equation of the path of the particle. Show the path on a graph.

Answer 1

y = - 2 $co{s}^2\pi t$
= -2 (1 - 2 $si{n}^2\pi t$)
= -2 $(1-2{\left(\frac{-x}{8}\right)}^2)$ ($\because sin\pi t$ = $-x/8$)
= -2 + $\frac{x^2}{16}$
This is the equation of path, which is a parabola. The path of the particle is shown in Fig.