Derive a model for a horizontal mass-spring system. Choose a mass value, a spring from a spring supplier (e.g. century spring, gutekunst) with its spring rate, and a force magnitude.

a. Show your derivation with your differential equation model (50 points) List the part number and give a link to the spring you chose.** b. What is the steady state position of your mass? (5 points) c. What is the order of the system and how do you know? (5 points) d. What is an assumption made by your model? (5 points) e. What is a limitation of your model? (5 points) f. Explain in your own words what a step input for this model would be (5 points)