Question

Find the ratio of time periods of two identical springs if they are first joined in series & then in parallel & a mass m is suspended from them:

• A. 4
• B. 2
• C. 1
• D. 3

Answer 1

Answer: (B)

2

When they are joined in series, the resultant spring constant $k_1$ is $\frac{k}{2}$.
When they are joined in series, the resultant spring constant $k_2$ is $2k$.
and frequency of spring mass system is given by
$\nu =\frac{1}{2\pi }\sqrt{\frac{k}{m}}\Rightarrow \nu \propto \sqrt{k}$
$\Rightarrow \frac{{\nu }_1}{{\nu }_2}=\sqrt{\frac{k_1}{k_2}}=\sqrt{\frac{\left(\frac{k}{2}\right)}{2k}}=\frac{1}{2}$
so the correct answer is 'B'