An object oscillates with simple harmonic motion along the \( x \) axis. Its position varies with time according to the equation \( x=(4.00) m \cos \left(\pi t+\frac{\pi}{4}\right) \) where \( t \) is in seconds and the angles in the parentheses are in radians.
a) Determine the amplitude, frequency, and period of the motion.
b) Calculate the velocity and acceleration of the object at any time \( t \).
c) Using the results of part (b), determine the position, velocity, and acceleration of the object at \( t=1.00 \mathrm{~s} \).
d) Determine the maximum speed and maximum acceleration of the object.