# 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,

$F$ = $-kx$

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 $t$ =$T_1$, if we take the projection along x-axis it is in positive x-direction and having positive velocity. Similarly, at $t$ = $T_2$ , 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

$F_2$ = $F_2=-k_2x$ (Towards left)

Force exerted by $S_1$ ,

$F_1$ = $-k_1x$ (Towards left)

So the total restoring force $(F)$ =$F_1 + F_2$

$F$ = $- (k_1 + k_2) x$

Hence, equivalent $k$ = $k_1 + k_2$

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,

$T$ = $2π\sqrt{\frac{m}{k}}$

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.