Question

some springs are combined in series and parallel arrangement as shown in figure iand a mass m is suspended from them. The ratio of their frequencies will be :

• A. 1 :1
• B. 2 :1
• C. $\sqrt{3}:2$
• D. 4 :1

Answer 1

The correct option is C $\sqrt{3}:2$

$\begin{array}{c}{T}_1=2\pi \sqrt{\frac{qm}{K}}\\ T_2=2\pi \sqrt{\frac{3m}{2K}}\\ \therefore \frac{T_1}{T_2}=\sqrt{\frac{2\times 2}{3}}=\frac{2}{\sqrt{3}}\\ \therefore \frac{f_1}{f_2}=\frac{\sqrt{3}}{2}\\ Hence,\\ optionCiscorrectanswer.\end{array}$