A) 0.72 sec
B) 0.64 sec
C) 0.48 sec
D) 0.36 sec
Correct Answer: C
Solution :
Under the influence of one force \[{{F}_{1}}=m\omega _{1}^{2}y\] and under the action of another force, \[{{F}_{2}}=m\omega _{2}^{2}y\]. Under the action of both the forces \[F={{F}_{1}}+{{F}_{2}}\] \[\Rightarrow \] \[m{{\omega }^{2}}y=m\omega _{1}^{2}y+m{{\omega }^{2}}y\] \[\Rightarrow \] \[\omega _{1}^{2}+\omega _{2}^{2}\]\[\Rightarrow \] \[{{\left( \frac{2\pi }{T} \right)}^{2}}={{\left( \frac{2\pi }{{{T}_{1}}} \right)}^{2}}+{{\left( \frac{2\pi }{{{T}_{2}}} \right)}^{2}}\] \[\Rightarrow \] \[T=\sqrt{\frac{T_{1}^{2}T_{2}^{2}}{T_{1}^{2}+T_{2}^{2}}}\] \[=\sqrt{\frac{{{\left( \frac{4}{5} \right)}^{2}}{{\left( \frac{3}{5} \right)}^{2}}}{{{\left( \frac{4}{5} \right)}^{2}}+{{\left( \frac{3}{5} \right)}^{2}}}}=0.48\sec \]
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