Amass 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 = 0.0360 m. (a) determine the location of the mass at t = 5.47 s? (b) determine if the mass is moving in the positive or negative x direction at t = 5.47 s? positive x direction negative x direction

b) The mass is moving in the positive x direction at t=5.47s

Explanation:

The position of an object that describes a simple harmonic movement as a function of time is given by the equation:

Where:

Let's asume A=1. Now, we need to find ω. So, let's use the next equation:

Where:

So:

We need to calculate Φ as well, so let's use the information provide by the problem:

Arccosine to both sides:

We are ready to evaluate the function x(t) at t=5.47:

The minus sign in the answer tell us that the mass is moving  in the negative x direction.