A) \[2\sqrt{2}\,rad/\sec \]
B) \[2\,rad/\sec \]
C) \[1\,rad/\sec \]
D) \[4\,rad/\sec \]
Correct Answer: A
Solution :
\[\therefore \,\,-{{e}^{-2x}}\,.{{y}^{2}}=2\ell n\,\,y-1\] \[\Rightarrow \,\,{{y}^{2}}={{e}^{2x}}\,-2{{e}^{2x}}\,\ell ny\] \[\omega ={{x}_{1}}+i{{y}_{1}}\,\] \[z={{x}_{2}}+i{{y}_{2}}\] at \[(1+2i)\,({{x}_{1}}+i{{y}_{1}})\,\] \[\Rightarrow \,2{{x}_{1}}+{{y}_{1}}=0\] Hence U is minimum at x = 0 Hence \[\Rightarrow \,2{{x}_{2}}\,+{{y}_{2}}=0\] is stable equilibrium position \[\therefore \,\,2{{x}_{1}}+{{y}_{1}}=2{{x}_{2}}+{{y}_{2}}\] when x is very small x3 can be neglected \[\Rightarrow -2({{x}_{2}}-{{x}_{1}})\,={{y}_{2}}-{{y}_{1}}\] \[\Rightarrow \,\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}\,=-2\]
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