The displacement x (in centimetres) of an oscillating particle varies with time t (in seconds) as  $x=2\cos \left(0.5\mathrm{\pi }t+\frac{\pi }{3}\right)$.

The magnitude of the maximum acceleration of the particle is:

Given     $x=2\cos \left(0.5\pi t+\frac{\pi }{3}\right)$

Velocity  $v=\frac{dx}{dt}$

               $=-2\times 0.5\pi \sin \left(0.5\pi t+\frac{\pi }{3}\right)$

Acceleration, $a=\frac{dv}{dt}$

                        $=-2\times 0.5\pi \times 0.5\pi \cos \left(0.5\pi t+\frac{\pi }{3}\right)$

Maximum acceleration, $a_{max} = - 2 \times 0.5 \pi \times 0.5 \mathrm{\pi }$

                                                    $=-\frac{{\pi }^2}{2}{\mathrm{cms}}^{-2}$

Magnitude is   $\left|a_{max}\right|=\left|-\frac{{\pi }^2}{2}\right|$

                                  $=\frac{{\pi }^2}{2}{\mathrm{cms}}^{-2}$