Asmall object is attached to the end of a relaxed, horizontal spring whose opposite end is fixed. the spring rests on a frictionless surface. let the initial position of the object be defined as x-0. the object is pulled to position x = a and then released, after which it undergoes simple harmonic motion. in one full cycle of its motion, the total distance traveled by the object is 2 4 o 4a

The total distance traveled by an object attached to a spring that is pulled to position x=A and then released is 4 A.

Explanation:

We have an small object attached to a relaxed spring whose opposite end is fixed. The spring rests on a frictionless surface. This means the only force acting on the object is the elastic  force of the spring, a conservative force, since the weight and the normal force compensate between them.

The initial position of the object is x=0 then is pulled to position x=A and released. After which it undergoes a simple harmonic motion with an amplitude A. From the position x=A to the equilibrium position in x=0 the object travels a distance A. From the equilibrium position x=0 to maximum negative position in x= -A the object travels again a distance A. Then to return to the original position the object should travel a distance 2 A in reverse direction.

In one full cycle of its motion the object travels a distance 4 A.

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orange juice however is a 95% liquid and has a very low viscosity