The displacement x (in centimetres) of an oscillating particle varies with time t (in seconds) as
x=2 cos(0.5πt+π3)
The magnitude of the maximum acceleration of the particle in cms−2 is
π22
Given that, x=2 cos(0.5πt+π3)
∴ Velocity, v=dxdt=−2×0.5π sin(0.5πt+π3)
and acceleration, a=dvdt=−2×0.5π×0.5πcos(0.5πt+π3)
∴ Maximum acceleration, amax=−2×0.5π×0.5π=−π22 cms−2
and the magnitude of maximum acceleration, |amax|=∣∣−π22∣∣=π22 cms−2
Hence, the correct choice is (c).