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Find the displacement of a simple harmon...

Find the displacement of a simple harmonic oscillator at which its PE is half of the maximum energy of the oscillator.

Text Solution

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PE of the oscillator at dispiacement y, `U=(1)/(2)momega^(2)y^(2)`
Maximum energy of the oscillator , `E=(1)/(2)momega^(2)A^(2)`
According to question,
`U=(1)/(2)E``(1)/(2)momega^(2)y^(2)=(1)/(4)momega^(2)A^(2)` `Rightarrow y=_(-)^(+)(A)/((sqrt2)`
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