5. The figure below shows a mass-spring model used in the design of packaging sy

Question

5. The figure below shows a mass-spring model used in the design of packaging systems and vehicle suspension systems. The springs exert a force that is proportional to their compression (Hooke's Law) with the proportionality constant being 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 is "gently" placed on the platform, it moves through a distance "x" before coming to rest. From statics, we know the weight force must balance the spring force(s) at this new position. Therefore: W-kix if x

Explanation / Answer

The function file is

function package(W,k1,k2,d);

if W<k1*d x = W/k1;

else x = (W+2*k2*d)/(k1+2k2);

end

disp('The distance travelled is:')disp(x)

Now in this session

>>package(400,10000,15000,0.1)

'The distance travelled is :'

0.040>>package(2500,10000,15000,0.1)

'The distance travelled is :' 0.1562

The function in above must be modified to provide an output variable x and to eliminate the display statements. So that is

function x= package(W,k1,k2,d);

if W<k1*d x= W/k1;

else x = (W+2*k2*d)/(k1+2*k2);

end

Here inputs must be in scalars since we used if statement.

W=0:5:3000;

plot(W,package(W,10000,15000,0.1))

The actual script file is follows

k1 = 10000;

k2 = 15000;

d = 0.1;

if k1*d<=3000 W = [0,k1*d,3000];

x = [package(W(1),k1,k2,d),package(W(3),k1,k2,d)]; plot(W,x,'-'),...xlabel(Weight(N)'),ylabel('Distance(m)')',...title('k1=10000,k2=15000,d=0.1')else W=[0,3000];

x = [package(W(1),k1,k2,d),package(W(2),k1,k2,d)]; plot(W,x,'-'),...xlabel(Weight(N)'),ylabel('Distance(m)')',...title('k1=10000,k2=15000,d=0.1')else W=[0,3000];

The script for the solution to the loop

W = linspace(0,3000,500); for k=1:500 x(k) = package(W(k), 10000,15000,0.1);

endplot(W,x)

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