Question

Two identical springs of spring constant $K$, each are connected in series and parallel as shown with a mass m. If the mass is slightly disturbed then the ratio of their frequencies of vertical oscillation will be

• A. 1 : 3
• B. 2 : 1
• C. 4 : 1
• D. 8 : 1

Answer 1

The correct option is B 2 : 1

For a suspended spring;
$T=2\pi \sqrt{\frac{m}{K_{eq}}}$
Caes-1: When spring is connected in series connection
$T_1=2\pi \sqrt{\frac{m}{K_1}}$ .....(1)
Where, $\frac{1}{K_1}=\frac{1}{K}+\frac{1}{K}$
$K_1=\frac{K}{2}$
on putting (1) equation (1)
$T_1=2\pi \sqrt{\frac{m}{\frac{k}{2}}}$
Case-2:
When spring is connected in parallel connection.
$T_2=2\pi \sqrt{\frac{m}{K_2}}$ .....(2)
Where, $K_2=K+K=2K$
putting $k_2$ value in equation (2)
$T_2=2\pi \sqrt{\frac{m}{2K}}$
On dividing equation (1) by (2)
$\frac{T_1}{T_2}=\sqrt{\frac{4}{1}}=2:1$