Answer to Question #123783 in Mechanics | Relativity for Ojugbele Daniel

Question

A particle performs a simple harmonic motion about a point x=0m, with amplitude 0.5m and frequency 4Hz. Given that it is momentarily at rest at x=0.5m with t=0s. Determine, the time required for the particle to move from point x=0 to a point 0.3m away.

Answer 1

$y=A\cos(\omega t+\phi)$

$t=0 \to y=0.5$

So,

$\phi=0$

$y=0.5\cos(2\pi\nu t)=0.5\cos(8\pi t)$

If $y=0$ then $t_0=1/16s=0.037s$

If $y=0.3$ then $t=\frac{1}{8\pi}\cos^{-1}(0.6)=0.0625s$

Finally

$\Delta t=0.0625-0.037=0.0255s$