Question

In figure $(A)$, mass ' $2\, m$ ' is fixed on mass ' $m$ ' which is attached to two springs of spring constant $k$. In figure $(B)$, mass ' $m$ ' is attached to two spring of spring constant ' $k$ ' and ' $2\, k$ '. If mass ' $m$ ' in $(A)$ and $(B)$ are displaced by distance ' $x$ ' horizontally and then released, then time period $T_1$ and $T_2$ corresponding to (A) and (B) respectively follow the relation.

• A. $\frac{T_1}{T_2}=\frac{3}{\sqrt{2}}$
• B. $\frac{T_1}{T_2}=\sqrt{\frac{3}{2}}$
• C. $\frac{ T _1}{ T _2}=\sqrt{\frac{2}{3}}$
• D. $\frac{ T _1}{ T _2}=\frac{\sqrt{2}}{3}$

Answer 1

Answer: (A)

$ T _1=2 \pi \sqrt{\frac{3 m }{2 k }}$
$ T _2=2 \pi \sqrt{\frac{ m }{3 k }} $
$ \frac{ T _1}{ T _2}=\frac{2 \pi \sqrt{\frac{3 m }{2 k }}}{2 \pi \sqrt{\frac{ m }{3 k }}}=\frac{3}{\sqrt{2}}$