Question

A body of mass ${}^{\prime }{m}^{\prime }$ hangs from three springs, each of spring constant ${}^{\prime }{K}^{\prime }$ as shown in the figure. If the mass is slightly displaced and let go, the system will oscillate with time period -

• A. $2\pi \sqrt{\frac{m}{3K}}$
• B. $2\pi \sqrt{\frac{3m}{2K}}$
• C. $2\pi \sqrt{\frac{2m}{3K}}$
• D. $2\pi \sqrt{\frac{3K}{m}}$

Answer 1

The correct option is B $2\pi \sqrt{\frac{3m}{2K}}$

From diagram
$\frac{1}{K_{eq}}=\frac{1}{K_1}+\frac{1}{K_2};\frac{1}{K_{eq}}=\frac{1}{K}+\frac{1}{2K}$
$K_{eq}=\frac{2}{3}K$
The system will oscillate with time period-
$T=2\pi \sqrt{\frac{m}{K_{eq}}}=2\pi \sqrt{\frac{3m}{2K}}$