Question

Consider two block system $ \frac{{{l}_{0}}}{2} $ and $ 2{{l}_{0}} $ . If $ {{I}_{0}} $ is removed suddenly, find the angular frequency and amplitude of $ 2{{l}_{0}}{{\cos }^{2}}\left( \frac{\pi y}{\beta } \right) $ .

• A. $ {{l}_{0}}{{\cos }^{2}}\left( \frac{\pi y}{\beta } \right) $ and $ \frac{{{l}_{0}}}{2}{{\cos }^{2}}\left( \frac{2\pi y}{\beta } \right) $
• B. $ 4{{l}_{0}}{{\cos }^{2}}\left( \frac{\pi y}{\beta } \right) $ and $ {{C}_{1}} $
• C. $ {{C}_{2}} $ and $ \frac{{{C}_{1}}}{{{C}_{2}}} $
• D. $ \frac{a}{b} $ and $ \frac{2a}{b} $

Answer 1

Answer: (B)

As $ {{m}_{2}} $ oscillates, angular frequency is $ \omega =\sqrt{\frac{k}{{{m}_{2}}}} $ or $ T=2\pi \sqrt{\frac{{{m}_{2}}}{k}} $ Amplitude = extra elongation due to $ {{m}_{1}} $ $ \therefore $ $ a=\frac{{{m}_{1}}g}{k} $