Question

Fig. given below, given the (x -t) plot of a particle executing one- dimensional simple harmonic motion. Given the sign of position,

Answer 1

In the S.H.M., acceleration, a = -ω²x, where ω (i,e., angular frequency) is constant.

(i) At time t = 0.3s, x is negative, the slope of x - t plot is negative hence position and velocity are negative. Since a = -ω²x, hence acceleration is positive.

(ii) At time t = 1.2 s, x is positive, the slope of x -1 plot is also positive, hence position and velocity are positive. Since, - ω²x, hence acceleration is negative.

(iii) At t = -1.2 s, x is negative, the slope of x - t plot is also negative. But since both x and t are negative here, hence velocity is positive. Finally acceleration 'a' is also positive.