Fig 2 (NCT).8 gives the ` x-t` plot of a particle executing one dimensional simle harmonic motion. Give the signs of position, velocity and acceleration variables of the particles at ` t= 0.3 s`, ` 1.2 s, - 1. 2 s`,

Explanation

In then S.H.M. acceleration ` a=- omega^@ x` , where omega 9i.e. angular frequency ) is constant.
(i) At time ` t= 0.3 s`, (x) is negative, the slope of ` x-t` plot is negative, hence position and velocity are egative. Since ` a =- omega^2 x`, hence, acceleration is positive.
(ii) AT time ` t= 1.2 s, x` is positive, the slope of ` x-t` plot is also positive, hence position and velocity are positive . Since ` a=- omega^2 x`, hence acceleration is negative.
(iii) At` t- 1.2 s, x`. is negative, the slpoe of ` x-t` plot is also negative . But since both (x) and (t) are negative here, hene velocity is positive, Finally acceleartion ` a` is also positive.