The position of a particle undergoing simple harmonic motion is given by \(x(t)=a \cos (b t+\pi / 3)\), where \(a=8.00 \mathrm{~m}\) and \(b=2.00 \mathrm{~s}^{-1}\). What are the 

(a) amplitude, 

(b) frequency \(f\),

(c) period?

(d) What are the speed and acceleration magnitude of the particle at \(t=\pi / 2 \mathrm{~s}\) ?

(e) What is its maximum acceleration magnitude, and at what instant after \(t=0\) does the particle first have this acceleration? 

(f) What is its maximum speed, and at what instant after \(t=0\) does it first have this speed?