8120T Problem 2 11 A system of springs is sho and k irof ing

8120T Problem 2 (11%): A system of springs is sho ,and k irof ings is shown in the figure, where ki -200, k2-80, ky-100. would be the forces F, F, and F\'j in order to ge spnt at Nodes 1, 2 and 3 are 23, nd u, 1, (1) what would be the forces r,, ), i spring forces in the ki and ka springs? ek and aninorder to generate the displacenent, ad (2) what are the

Solution

Let us start answering the question considering the spring k₅

Given spring rate k₅= 100 N/m

It is given that u3 = -1 m

Hence force exerted on the spring F = kx = 100 x -1 = -100 N

Now let us find the force acting on the spring k₃

It is given that u₁= 2 m

There is a u₃ = 1m acting on it compressing the spring making the total compressive displacement = 3m

Spring rate k₃= 100 N/m

Hence, the force acting on the spring k₃ = 300 N

Next stop is the spring k₁ with a spring rate of k₁= 200 N/m

Displacement acting on it = 2m

Hence force acting on teh spring k₁ is 400N

Next comes the spring k₂ with spring rate k₂=80 N/m

Dispacement experienced by it u₂ = 3m

Hence, force experienced by the spring k₂ is 240N

And lastly, we have the spring with spring rate k₄=40 N/m

It has a displacement of u₁=2 and u₂=3 in the same direction. This means that the spring is displaced by 2 m and the compression displacement of 1m

Hence, force inside spring k₄= 40N

Hence, the force acting on 1 is the sum of all forces experienced by it = 400+300+40 = 740N

to balance it, force of 740N in opp direction should be deployed which is +740N

Force on 2 is = 40 - 240 = -200N

Hence force deployed is 200N

Force on 3 = 300 +100 = 400N