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(A) When two springs with spring constant $K$ are connected in series,the equivalent spring constant $K_{eq}$ is given by the formula: $\frac{1}{K_{eq

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$1/2, \sqrt{2}$

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(A) When two springs with spring constant $K$ are connected in series,the equivalent spring constant $K_{eq}$ is given by the formula: $\frac{1}{K_{eq}} = \frac{1}{K} + \frac{1}{K} = \frac{2}{K}$.Therefore,$K_{eq} = \frac{K}{2}$. The new spring constant is changed by a factor of $1/2$.The time period of a spring-mass system is given by $T = 2\pi \sqrt{\frac{M}{K}}$.The new time period $T'$ with $K' = K/2$ is $T' = 2\pi \sqrt{\frac{M}{K/2}} = 2\pi \sqrt{\frac{2M}{K}} = \sqrt{2} 	imes (2\pi \sqrt{\frac{M}{K}}) = \sqrt{2}T$.Thus,the time period changes by a factor of $\sqrt{2}$.

If two similar springs each of spring constant $K$ are joined in series,the new spring constant and time period would be changed by a factor of:

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