Question

Position time relationship of a particle executing simple harmonic motion is given by the equation X = 2 sin( 50 πt+ 2π/3)where x is m and time t is in seconds. what is the position of particle at t=0.5 s?​

Answer 1

$x = 2 \sin(50\pi \: t + \frac{2\pi}{3} )$

$t = \frac{5}{10} = \frac{1}{2}$

$x = 2 \sin(50\pi \times \frac{1}{2} + \frac{2\pi}{3} )$

$2 \sin(25\pi + \frac{2\pi}{3} )$

$2 \sin( \frac{2\pi}{3} )$

$- 2 \times \frac{ \sqrt{3} }{2}$

$- \sqrt{3} \: m$