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  • For what value of displacement the kinetic energy and potential energy of a simple harmonic oscillation become equal ?   Option: 1 <str

For what value of displacement the kinetic energy and potential energy of a simple harmonic oscillation become equal ?
 
Option: 1 x=\frac{A}{2}
Option: 2 x=\pm A
Option: 3 x= 0  
Option: 4 x=\pm \frac{A}{\sqrt{2}}

Answers (1)

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\begin{array}{l} \mathrm{KE}=\mathrm{PE} \\ \Rightarrow \frac{1}{2} \mathrm{~m} \omega^{2}\left(\mathrm{~A}^{2}-\mathrm{x}^{2}\right)=\frac{1}{2} \mathrm{~m} \omega^{2} \mathrm{x}^{2} \\ \mathrm{~A}^{2}-\mathrm{x}^{2}=\mathrm{x}^{2} \\ 2 \mathrm{x}^{2}=\mathrm{A}^{2} \\ \mathrm{x}=\pm \frac{\mathrm{A}}{\sqrt{2}} \end{array}

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