Types of Force

SERIES COMBINATION OF SPRINGS: 

When same springs are connected as shown in the figure below, these are said to be connected in series. A constant force F is applied on  spring 2. So that the springs are extended and the total  extension of the combination is the sum of elongation of each spring.  Alternatively, the direction of force could be reversed so that the springs are compressed.
                           

This system of two springs in series is equivalent to a single spring, of spring constant k. The value of k can be found from the formula that applies to capacitors connected in series in an electrical circuit.
For spring-1, from Hooke’s Law    F=k₁x₁
where x₁ is the deformation of spring.
Similarly, if x₂ is the deformation of spring-2 we haveF=k₂x₂
Total deformation of the systemx₁+x₂=F/k₁+F/k₂
                    x₁+x₂=F(1/k₁+1/k₂)
Rewriting and comparing with Hooke’s law we get \( \frac{1} {k} = \frac{1} {{k_1 }} + \frac{1} {{k_2 }} \)