A mass attached to the end of a spring is oscillating with a period of 2.25 s on a horizontal frictionless surface. The mass was released from rest at t = 0 from the position x = 0.0700 m.(a) Determine the location of the mass at t = 5.31 s?(b) Determine if the mass is moving in the positive or negative x direction att = 5.31 s?

The mass is moving in the negative x direction

Explanation:

In a spring mass system, the position of the mass for every time is defined by:

The oscillation frequency can be written as:

And, since the period is the reciprocal of the frequency:

Using the previous equations and the data provided by the problem:

Therefore:

Evaluating t=5.31 into the motion equation:

Since the position for t=5.31 is negative, we can conclude that the mass is moving in the  negative x direction.