Question

All springs, string and pulley shown in figure are light. Initially when both the strings were on their natural state, the system was released from the rest. The maximum displacement of block as in $x\times \left(\frac{5mg}{k}\right)$. Calculate x

Answer 1

Given,

Maximum dipole moment is $A=x\times \left(\frac{5mg}{k}\right)$

At maximum displacement, the system is in equilibrium,

So, $M=2x_1+x_2$

$mg=k{x}_2\Rightarrow x_2=\frac{mg}{k}\Rightarrow mg+k{x}_2=k{x}_1$

$x_1=x_2+\frac{mg}{k}=\frac{2mg}{k}$

Since $x_2\Rightarrow A=2x_1+x_2=\frac{4mg}{k}+\frac{mg}{k}=\frac{5mg}{k}$

Therefore $X=1$