A spring is compressed between two toy carts of masses \[{{m}_{1}}\]and\[{{m}_{2}}\]. When the toy carts are released, the spring exerts on each toy cart equal and opposite forces for the same small time \[t\]. If the coefficients of friction \[\mu \] between the ground and the toy carts are equal, then the magnitude of displacements of the toy carts are in the ratio

• A. \[\frac{{{S}_{1}}}{{{S}_{2}}}=\frac{{{m}_{2}}}{{{m}_{2}}}\]       
• B. \[\frac{{{S}_{1}}}{{{S}_{2}}}=\frac{{{m}_{1}}}{{{m}_{2}}}\]
• C. \[\frac{{{S}_{1}}}{{{S}_{2}}}={{\left( \frac{{{m}_{2}}}{{{m}_{1}}} \right)}^{2}}\]
• D. \[\frac{{{S}_{1}}}{{{S}_{2}}}={{\left( \frac{{{m}_{1}}}{{{m}_{2}}} \right)}^{2}}\]