Consider two massless springs connected in series. spring 1 has a spring constant k1, and spring 2 has a spring constant k2. a constant force of magnitude f is being applied to the right. when the two springs are connected in this way, they form a system equivalent to a single spring of spring constant k.

Equivalent spring constant

Explanation: Spring constant, also known as stiffness constant is the amount of load (force) required to make a deformation of unit length in the size of  the spring from its free .

Mathematically given as:

...............(1)

In series the springs are connected back to back consecutively in a single line as shown in figure.

In such a case:

Mathematically represented as:

...........................(2)

∵ From eq. (1) & (2) we have,

              ∵F=-kx, where negative sign denotes that the restoration force acts in the direction opposite to the applied force.

∵The equivalent force is equal on each spring.

We get the relation as:

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