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Category > Computer Science Posted 14 Jul 2017 My Price 11.00

mass-spring system

We want to analyze the mass-spring system discussed in Problem 17 for the case in which the weight W is dropped onto the platform attached to the center spring. If the weight is dropped from a height h above the platform, we can find the maximum spring compression x by equating the weight’s gravitational potential energy W(h + x) with the potential energy stored in the springs. Thus

which can be solved for x as

which gives the following quadratic equation to solve for x:

a. Create a function file that computes the maximum compression x due to the falling weight. The function’s input parameters are k1, k2, d, W, and h. Test your function for the following two cases, using the values k1 = 104 N/m; k2 = 1.5 × 104 N/m; and d = 0.1 m.

b. Use your function file to generate a plot of x versus h for 0 ≤h≤ 2m. Use W = 100 N and the preceding values for k1, k2, and d.

Problem 17

Figure P17 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

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.

Answers

Maurice Tutor
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Status NEW Posted 14 Jul 2017 11:07 PM My Price 11.00

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