The position of a particle undergoing simple harmonic motion is given by \(x(t)=20 \cos (8 \pi t)\), where \(x\) is in millimeters and \(t\) is in seconds. For this motion, what are the 

(a) amplitude, 

(b) frequency \(f\), 

(c) period? 

(d) What are the first three instants at which the particle is at \(x=0\) ? 

(e) Determine the \(x\) components of position, velocity, and acceleration of the particle at t=0.75 s.