Question

# What is the total distance traveled by an object moving back and forth in simple harmonic motion in a time interval equal to its period when its amplitude is equal to A?

Solution

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The amplitude $A$ of an object in simple harmonic motion is the maximum displacement from the origin (or starting point).

In one period of simple harmonic motion, the object starts from origin, moves in the forward direction to its maximum displacement, comes back to the origin, moves in the backward direction to its maximum displacement and returns back to the origin. The distance traveled by the object in one period is $4A$.

As an example a ball connected to an elastic string is shown below. The ball starts at $t=0$ from $y=0$. At the end of one cycle, that is, at $t=T$, the ball comes back to $y=0$. The total distance traveled by the ball is $4A$.

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