You are in charge of drinks at the graduation dinner and the people want carbonated root beer. You come up with the ingenious idea of freezing a
100 kg
block of dry ice on the end of a spring and immersing the spring-mass system in a large vat containing the root beer. You pull the dry ice down 1 meter and let it go. The dry ice melts so that the mass of dry ice, as a function of time, is given by
m(t)=100− 2
1
​
t
where
t
is in minutes. The friction coefficient is 1 and the spring constant increases as the spring gets cold, so it is given by
k(t)=2t+1
. a. Create an IVP which models this situation. b. Derive the power series solution to the IVP. c. What is the position of the dry ice after 1 minute? If your answer is approximate, explain how far off you believe you are from the true value and why. d. Sketch the graph of the motion of the dry ice for the first few minutes. Explain how you got your graph and for how many minutes you believe the graph is reasonably accurate. Explain how you came up with the number of minutes.