A small object is attached to the end of a horizontal spring at position x = 0. It is the pulled to position x = A and released. In one full cycle of its motion, the total distance traveled by the object is...
4A
The object starts at -A, travels past zero to A--at which point the object has traveled the distance 2A. It must then travel back to complete the cycle of motion giving it a final distance of 4A
To determine the total distance traveled by the object in one full cycle of its motion, we need to understand the characteristics of simple harmonic motion.
In a simple harmonic motion, such as the motion of an object attached to a spring, the object oscillates back and forth around its equilibrium position. This motion can be described by a sine or cosine function.
In this case, the object is attached to the end of a horizontal spring and pulled to a position x = A. Let's assume that the equilibrium position of the system is x = 0. When the object is released, it will start oscillating around this equilibrium position.
During one full cycle of its motion, the object moves from position x = A to x = -A, and then back to position x = A. The object passes through the equilibrium position twice, once as it moves from x = A to x = -A, and then again as it moves from x = -A to x = A.
Therefore, the total distance traveled by the object in one full cycle of its motion is the sum of the distances traveled as it moves from x = A to x = -A and from x = -A to x = A.
The distance between x = A and x= -A is 2A, so the object travels a distance of 2A from x = A to x = -A. Similarly, it also travels a distance of 2A from x = -A to x = A.
Therefore, the total distance traveled by the object in one full cycle of its motion is 2A + 2A = 4A.