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A body is executing simple harmonic motion. At a displacement `x` its potential energy is `E_(1)` and at a displacement `y` its potential energy is `E_(2)` The potential energy `E` at displacement `(x+y)` isA. `E_(1)+E_(2)`B. `sqrt(E_(1)E_(2))`C. `sqrt(E_(1)^(2)+E_(2)^(2))`D. `E_(1)+E_(2)+2sqrt(E_(1)E_(2))` |
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Answer» Correct Answer - D `E_(1)=(1)/(2)momegat^(2)x^(2), E_(2)=(1)/(2)momega^(2)y^(2)` `:. sqrt(E_(1)E_(2))=[(1)/(2)m omega^(2)x^(2)xx(1)/(2)m omega^(2)y^(2)]^(1//2` `=(1)/(2)momega^(2)xy` `E=(1)/(2)momega^(2)(x+y)^(2)=(1)/(2)momega^(2)(x^(2)+y^(2)+2xy)` `(1)/(2)momega^(2)x^(2)+(1)/(2)momega^(2)y^(2)=2xx(1)/(2)momega^(2)xy` `=E_(1)+E_(2)+2sqrt(E_(1)E_(2))` |
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