Answer: Equivalent spring constant [tex]{k_{eq}}=\frac{1}{k_{1}}+\frac{1}{k_{2}}[/tex]
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:
[tex]F=-kx[/tex] ...............(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:
[tex]x_{eq}=x_{1}+x_{2}[/tex] ...........................(2)
∵ From eq. (1) & (2) we have,
[tex]x_{eq}=x_{1}+x_{2} [/tex] ∵F=-kx, where negative sign denotes that the restoration force acts in the direction opposite to the applied force.
[tex]\Rightarrow \frac{F_{eq}}{k_{eq}}=\frac{F_{1}}{k_{1}}+\frac{F_{2}}{k_{2}}[/tex]
∵The equivalent force is equal on each spring.
We get the relation as:
[tex]\Rightarrow\frac{1}{k_{eq}}=\frac{1}{k_{1}}+\frac{1}{k_{2}}[/tex]
