Introduction to Spring Constant

In the last article, we learnt the basic concepts of SHM. Now we shall try to visualise the spring-mass system. Before that, we will see what spring constant is. Force by the action of the spring is given by,

k is known as the spring constant or stiffness constant.

Unit of spring constant is N/m.

There are different types of spring. For example torsion spring which works due to turning of the spring.

We can also visualise this spring-mass motion with the help of uniform circular motion.

Suppose at t = 0, the particle is as shown in the figure. If we take the projection of that on the x-axis it is at origin. At t = T₁, if we take the projection along x-axis it is in positive x-direction and having positive velocity. Similarly, at t = T₂, the projection is in negative x-axis and having negative velocity. By observing this we can say we take the projection of uniform circular motion on the x-axis it represents an SHM. Sometimes this approach is very useful in solving the numerical problem as compared to equation-based approach.

How to find spring constant when a number of springs are connected together? Suppose we have a situation as shown below:

Spring-mass system 1

Suppose the mass is displaced by x towards right, so the force exerted by S₂,

Force exerted by S₁,

So the total restoring force (F) = F₁ + F₂

Hence, equivalent k = k₁ + k₂

Using a similar approach try to find equivalent spring constant for the following?

Also, the time period for the spring mass system can be shown to be,

Where k is the equivalent stiffness constant.

The relationship between the spring constant and the displacement is explained in the video with the help of a spring balance

Stay tuned with BYJU’S to learn more about spring constant, SHM and much more.