A body oscillates with S.H.M according to the equation $\mathrm{x}=6 \cos \left(3\mathrm{\pi t}+\frac{\mathrm{\pi }}{3}\right) \mathrm{cm}$ 

The displacement velocity and acceleration at time t=2 sec. in magnitude are

displacement at time ‘t’=2 sec:

 $\mathrm{x}(\mathrm{t}=2)=6\cos \left(6\mathrm{\pi }+\frac{\mathrm{\pi }}{3}\right)=3 \mathrm{cm}$ 

(ii) Velocity at time t = 2 sec = velocity at position x=3 cm:

 $\mathrm{v}\left(\mathrm{x}\right)=\mathrm{\omega }\sqrt{{\mathrm{A}}^2-{\mathrm{x}}^2}$

Here $\mathrm{\omega }=3\mathrm{\pi };\mathrm{A}=6,$

$\Rightarrow \mathrm{v}(\mathrm{x}=3)=3\mathrm{\pi }\sqrt{36-9}=9\mathrm{\pi }\sqrt{3} \mathrm{cm}/\sec$

(iii) Acceleration: $a={\mathrm{\omega }}^2\mathrm{x}=27{\mathrm{\pi }}^2 \mathrm{cm}/{\sec }^2$