In the diagram shown, no friction at any contact surface. Initially, the spring has no deformation. What…

In the diagram shown, no friction at any contact surface. Initially, the spring has no deformation. What will be the maximum deformation in the spring? Consider all the strings to be sufficiently large. Consider the spring constant to be $K$.

1. $\frac{4F}{3K}$
2. $\frac{8F}{3K}$
3. $\frac{F}{3K}$
4. None

Solution

$a_{COM}=\frac{F}{3M}$

with respect to the Center of mass



$\frac{4F}{3}{X}_1+\frac{4F}{3}{X}_2=\frac{1}{2}K{\left(X_1+X_2\right)}^2$

$\frac{8F}{3K}=\left(X_1+X_2\right)$

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