The x - t graph of a particle performing simple harmonic motion is shown in the figure. The acceleration of the particle at t = 2   s is:

Step-by-step solution

From the figure, it can be concluded that A = 1 ω = 2 π 8 = π 4 Hence, the equation of motion of the particle is given by x = A sin ω t = sin π 4 t       . . . 1 The velocity of the particle is, then, given by v = d x d t = d d t sin π 4 t =   π 4 cos π 4 t       . . . 2 Hence, the acceleration of the particle can be written as a = d v d t = d d t π 4 cos π 4 t = - π 2 16 sin π 4 t       . . . 3 Substitute