Serway & Jewett — Oscillatory Motion: Problem 43

Your father is preparing the backyard for the installation of new sod. He has finished cleaning the ground of roots and rocks, has raked it to the correct contours, and now must pull a heavy roller, shown in Figure P15.43a, over the ground several times to flatten and compact the dirt. He is tired after all of his work and asks you to do the rolling for him. He tells you that each section of the yard must be rolled over ten times with the roller. You are tired from your physics studying, but decide you can use your understanding of physics to make the job easier. You attach the roller to a spring as shown in Figure P15.43b, with the other end attached to a post pounded into the ground. You then just pull the roller out once and let it oscillate over each part of the yard for ten rolls while you sit back and relax. Before beginning, you wonder how much time you will have to relax at each location before you have to move the post and roller to a new location. The mass of the roller is \(M = 400 \text{ kg}\), and the spring constant is \(k = 3\,500 \text{ N/m}\). The flat, smooth ground supplies enough friction that the roller rolls instead of sliding, but the rolling friction is negligible.