Question

What is the total distance travelled by an object executing simple harmonic motion in a time equal to its time period when amplitude is x

Answer 1

Simple harmonic motion means the motion can be described as a sum of sines and cosines or just a sine or cosine with a phase angle thrown in. Therefore, if the time elapsed is equal to its period, this is equal to performing a full rotation on the unit circle or in terms of a oscillator: going up to A down A then down another A and then up an A.

Therefore the total distance traveled is 4A.