The displacement (x) of a particle as a function of time (t) is given by x = a sin (bt + c)where a, b and c are constants of motion. Choose the correct statements from the following.

The motion of the particle is simple harmonic. The displacement at time t is: x = a sin (bt + c)Therefore, displacement at time (t+(2π/b)) isx at t+2πb=asin⁡bt+2πb+c=asin⁡[bt+c+2π]=asin⁡(bt+c)=x( at time t)Hence, statement (a) is correct.Statement (b) is also correct since the same displacement is recovered after a time interval of (2π/b). Statement (c) is correct  because the velocity is zero when the displacement = ±the amplitude, i.e.. at the extreme ends of the motion. Statement (d) is incorrect, because the acceleration is maximum (in magnitude) at r =±a.