Figure below 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. (if x=d) These relations can be used to generate the plot of x versus W. (a) The following values are given: k1=104 N/m; k2 = 1.5 *104 N/m; d =0.1 m. Create a function that computes the distance x, using the input parameter W; Then, test your function for the following two cases, using the values: W=500 N W=2000 N. (b) Create another script and 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 below 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. (if x=d) These relations can be used to generate the plot of x versus W. (a) The following values are given: k1=104 N/m; k2 = 1.5 *104 N/m; d =0.1 m. Create a function that computes the distance x, using the input parameter W; Then, test your function for the following two cases, using the values: W=500 N W=2000 N. (b) Create another script and 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.
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