1. (5 pts) An undamped spring-mass system with mass $m = 2kg$ and spring constant $k = 8N/m$ is at equilibrium position and is not moving at $t = 0$. No force is acted on the mass for the first $t = 10$ seconds. Then, a force $f(t) = 40 N$ is applied to the mass. At $t = 15$ and later, the force drops to zero.
a) (2 pts) Set up the model for this situation and find the position function of the mass BY HAND.
b) (2 pts) In python, follow similar procedure as we did in class: find the Laplace transform of the input and the inverse transform of the output. Then, plot the input and the output together on the same graph for $0 \le t \le 25$ (sec).
c) (1 pts) Interpret your results.