A mass $0.9 \mathrm{kg}$ attached to a horizontal spring, executes SHM with an amplitude ${\mathrm{A}}_1$. When this mass passes through its mean position, then a smaller mass of 124 g is placed over it and both masses move together with amplitude ${\mathrm{A}}_2$. If the ratio $\frac{{\mathrm{A}}_1}{{\mathrm{A}}_2}$ is $\frac{\mathrm{\alpha }}{\mathrm{\alpha }-1},$ then the value of $\alpha$ will be