# Introduction To Spring Constant

In the last article we learnt the basic concepts of SHM. Now we shall try to visualize the spring mass system. Before that we will see what spring constant is. We know force by a 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 visualize 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 projection of a uniform circular motion on the x-axis it represents an SHM. Sometimes this approach is very useful in solving 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:

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 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.