The displacement time (x-t) graph of a particle performing simple harmonic motion is shown in the figure. The acceleration fo the particle at t = 1 s is

Step-by-step solution

From the given displacement-time graph, the amplitude of the simple harmonic motion is A = 2 m. The time period of the motion is T = 4 s. The angular frequency is given by = 2 T = 2 4 = 2 rad/s. The acceleration of a particle in SHM is given by a = - ^2 x . At t = 1 s, the displacement of the particle is x = +2 m (as seen from the graph). Substituting the values, we get: a = - ( 2 )^2 2 a = - ^2 4 2 = - ^2 2 m/s ^2 . Answer: - ^2 2 m/s ^2