Question

As shown in figure, two light springs of force constant $300\text{N/m}$ and $600\text{N/m}$ oscillate a block of mass $10\text{kg}$. Find the effective force constant.

• A. $150\text{N/m}$
• B. $200\text{N/m}$
• C. $300\text{N/m}$
• D. $600\text{N/m}$

Answer 1

The correct option is B $200\text{N/m}$

Given,
Force constant of spring 1 $\left(K_1\right)=300\text{N/m}$
Force constant of spring 2 $\left(K_2\right)=600\text{N/m}$
Mass of block $\left(m\right)=10\text{kg}$
In series arrangement,
effective spring constant $\left(K\right)=\frac{K_1{K}_2}{K_1+K_2}$
$=\frac{300\times 600}{900}$
$=200\text{N/m}$