Exploring Vibrations and Oscillations with a Mass-Spring System

What is the location and speed of a 0.320 kg mass attached to a 412 N/m spring after 36.5 s?

A 0.320 kg mass attached to a 412 N/m spring starts at its maximum amplitude of 0.160 m after 36.5 s. What is its location at this instant? What is its speed?

Answer:

At the given instant of 36.5 seconds, the location of the mass attached to the 412 N/m spring is -0.149 m to the left of the equilibrium position. Its speed at this same time is 4.38 m/s.

In this scenario, we are dealing with a mass-spring system consisting of a 0.320 kg mass and a spring with a stiffness of 412 N/m. The system begins at its maximum amplitude, indicating that the mass is at its farthest distance from the equilibrium point. This amplitude is measured as 0.160 m. After 36.5 seconds, the mass's location is specified as -0.149 m, suggesting that it has moved to the left of the equilibrium position. The negative sign indicates the direction of displacement. Additionally, the mass's speed at this moment is determined to be 4.38 m/s, reflecting the magnitude of its velocity. Understanding the behavior of mass-spring systems can provide valuable insights into the world of vibrations and oscillations. By analyzing parameters such as location and speed at specific time points, we can gain a deeper understanding of the dynamics at play.