Figure P20 shows a mass-spring model of the type used

Figure P20 shows a mass-spring model of the type used to design packaging systems and vehicle suspensions, for example. The springs exert a force that is proportional to their compression, and the proportionality constant is the spring constant k. The two side springs provide additional resistance if the weight W is too heavy for the center spring. When the weight W is gently placed, it moves through a distance x before coming to rest. From statics, the weight force must balance the spring forces at this new position. Thus

W = k₁x if x < d

W = k₁x + 2k₂(x – d) if x ≥ d

These relations can be used to generate the plot of x versus W.

a. Create a function le that computes the distance x, using the input parameters W, k₁, k₂, and d. Test your function for the following two cases, using the values k₁ = 10⁴ N/m; k₂ = 1.5 × 10⁴ N/m; d = 0.1 m.

W = 500 N

W = 2000 N

b. Use your function to plot x versus W for 0 ≤ W ≤ 3000 N for the values of k₁, k₂, and d given in part a.

Figure P20