In the spring arrangement shown in the Figure 1 the displace

In the spring arrangement shown in the Figure (1), the displacement x is caused by the applied force f. Obtain the deflection x of the system model as a function of the applied force f. Assume that each spring exerts a force that is proportional to its compression, and the system is in static equilibrium.

Solution

As we can see from the above figure that spring 2 is not in contact of the moving part of the body so it will not provide any restraining force.

We will find the equivalent spring constant of the above model

The total force is f so it will be shared by two springs

So

Let ke be the equivalent stiffness

Ke*x= k1*x+k2*x

Therefore

Ke=k1+k2

And

x=f/(k1+k2)

Or

x=f/2k