An object undergoes simple harminic motion of amplitude A. Through what total distance does the object move during one complete cycle of its motion?

Answer 1

say it is

y = A sin w t

goes up A to sin 90 degrees
goes down A to sin 180 degrees
goes down another A to sin 270 dgrees
goes back up A to sin 360 or zero degrees and starts again
up A
down 2A
up A
moved total of 4 A

Answer 2

4A