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 \[\frac{2a}{b}\]
Correct Answer: B
Solution :
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 \[{{m}_{1}}\] \[\therefore \] \[a=\frac{{{m}_{1}}g}{k}\]
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