From the figure, it can be concluded that
Aω===182π4π
Hence, the equation of motion of the particle is given by
x==Asinωtsin4πt...(1)
The velocity of the particle is, then, given by
v===dtdxdtd(sin4πt)4πcos4πt...(2)
Hence, the acceleration of the particle can be written as
a===dtdvdtd(4πcos4πt)−16π2sin4πt...(3)
Substitute 2 for t into equation (3) to calculate the required value of the acceleration.
a==−16π2sin(4π×2)−16π2ms−2