15A – SHM
Situation:
You are assigned to take over a project that is partially completed. An object called the “spring” was discovered deep in
the Pacific Ocean near the Marianas Trench. What follows are transcripts of the audio logs that we recovered. Find out
everything you can about the “spring”. Write a report that details each test along with the results (Explain in words what
you are doing so that a random person with basic physics knowledge can understand.) Submit the document to moodle.
Log 1:
The spring measures 0.75 meters in length but has a very small mass. We suspended the spring vertically from the ceiling
of a room that has a height of 3 meters. A 0.5 meter cube with a mass of 2 kg was attached to the bottom of the spring.
When attached to the spring, the bottom of the mass rested 1.5 meters above the floor. From this we were able to
determine the spring constant … static…
𝐴𝑛𝑠𝑤𝑒𝑟: 78.4
𝑁
𝑚
Log 2:
The goal of Test 2 was to measure the response of the spring to extension. We followed the procedure from Test 1, and
again the bottom of the cube rested 1.5 meters above the ground. We pulled the cube down to where it was 1 meter above
the ground. We released the cube and to our amazement, the spring (with cube attached) underwent simple harmonic
motion. With my watch I was able to measure the period of oscillation … static…
𝐴𝑛𝑠𝑤𝑒𝑟: 𝑇 = 1𝑠
Log 3:
We decided to use our special sonar tracking system to measure spring’s oscillation. The tracking system has a super thin
sensor that we placed under the oscillating spring plus cube system. The sensor emits sound pulses toward the cube. The
sensor then detects the pulses that get reflected back. With that information, the sensor can tell us the exact position of the
cube and spring at any given time. Unfortunately, someone let the new guy push the button to start the tracking system.
As a result our first time, t = 0 seconds, happened when the cube was 1.7 meters away from the sensor and on its way
down. We were able to create an equation to describe the motion of the spring (Check with the instructor before plotting).
Figure 1 of my report is a plot of the position vs time of the spring motion. Note that we have chosen y = 0 to be the
𝑇
equilibrium position of the spring plus cube system. The time per data point is 4 and the plot extends for 2 periods (8
points).
𝐴𝑛𝑠𝑤𝑒𝑟: 𝜙𝑖 = 2.73 𝑟𝑎𝑑𝑖𝑎𝑛𝑠
Log 4:
In this test we wanted to study how the spring energy changes throughout its oscillation. We found the locations where the
kinetic and potential energies were maximized. In addition, we found that the total energy of the system … static…
𝐴𝑛𝑠𝑤𝑒𝑟: 𝐸𝑡𝑜𝑡𝑎𝑙 = 9.8 𝐽