solution

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

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

a. Create a function file 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.

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.