A) 16 unit
B) 6 unit
C) 4 unit
D) 8 unit
Correct Answer: D
Solution :
The equation of displacement \[{{x}_{1}}=4\sin \left( 10t+\frac{\pi }{6} \right)\] The energy of this equation \[{{E}_{1}}=\frac{1}{2}mw_{1}^{2}a_{1}^{2}\] \[=\frac{1}{2}m\times 10\times 10\times 4\times 4\] The second equation of displacement \[{{x}_{2}}=5\cos (\omega t)\] The energy of this equation \[{{E}_{2}}=\frac{1}{2}m\omega _{2}^{2}a_{2}^{2}\] \[=\frac{1}{2}m\omega _{2}^{2}\times 5\times 5\] According to question \[\because \] \[{{E}_{1}}={{E}_{2}}\] \[\therefore \]\[\frac{1}{2}m\omega _{2}^{2}\times 5\times 5=\frac{1}{2}m\times 10\times 10\times 4\times 4\] \[\omega _{2}^{2}=\frac{10\times 10\times 4\times 4}{5\times 5}\] \[\omega _{2}^{2}=2\times 2\times 4\times 4\] Or \[{{\omega }_{2}}=\sqrt{2\times 2\times 4\times 4}\] \[=2\times 4=8\]unit
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