In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression x ( t ) = 15.0 cos( 20.0 t ) where x is in centimeters and t is in seconds.

(a) What is the period of the motion?

(b) What is the amplitude of the motion?

(c) At t = 1 s, find the position of the piston.

(d) At t = 1 s, find the velocity of the piston.

(e) At t = 1 s, find the acceleration of the piston.

(f) Sketch a plot of the acceleration as a function of time. Scale the plot properly.