Question

In the figure shown, the entire arrangement is on smooth horizontal surface. The mass of rod \( O A \) is negligible and it can freely rotate about \( O \), block \( B \) of mass \( m \) is attached to spring (2). Spring constants of springs are shown in figure. Now the block is slightly displaced along the length of the spring (2) and released. Block performs simple harmonic motion with time period \( 2 \pi \sqrt{\frac{ Cm }{ K }} \), find \( C \).

Answer 1

 

\(f= -8kx\)

\(ma = - 8kx\)

\(a = \frac{-8k}mx\)

\(w^2 = \frac{8k}m\)

\(T =\frac{2\pi }w\)

⇒ \(2\pi \sqrt{\frac m{8k}}\)

\(T = 2\pi \sqrt{\frac{2m}{16k}}\)

Then 

C = 2