Although we cannot do labs in person this semester, we can walk through the findings of another group of Diff Eq students. Using the data they collected, you will be asked to answer questions to this lab. The full lab can be viewed here. Here is a summary of the findings: Logger Pro created a line of best fit for the data points gathered from analyzing a video of the spring oscillating with a mass. The equation for theline of best fit was determined to be y $=0\mathrm{.}038$ sin$(9\mathrm{.}56$t $+0\mathrm{.}20)-0\mathrm{.}09,$ where t is time in seconds andy is displacement in meters. The team used a $1$ kilogram mass which displaced the spring $0\mathrm{.}09$ metersbelow equilibrium. We can use their initial conditions of y$(0)=-0\mathrm{.}083$ and the fact that the spring wasreleased from rest $-$ thus y$\text{'}(0)=0.$ Your job is to build the equation of motion for this spring. Thedamping coefficient c is unknown, but can you make a decent estimate for the value of c$?$ Please consider whether the spring should be under$/$over$/$critically damped based on what you understand of the context. This can help you determine a value, or at least a range of possible values, for c$.$ Compare and contrast the two displacement models. What caused the differences? Which one do you think is better?