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Question
The displacement of a particle performing simple harmonic motion is `1/3` rd of its amplitude. What fraction of total energy will be its kinetic energy?
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Solution
Given:
`x = A/3`
To find:
Fraction of T. E. = ?
Formula:
Total energy (T. E.) = `1/2 kA^2` ...(i)
Kinetic energy (K. E.) = `1/2 k (A^2 - x^2)` ...(ii)
Putting `x = A/3`
∴ K. E. = `1/2K[A^2 - (A/3)^2]`
= `1/2 KA^2[1 - 1/9]`
= `1/2KA^2(8/9)`
∴ K. E. = `8/18 KA^2` ...(iii)
Dividing equation (iii) and (i)
`("K. E.")/(T. E.") = (8/18 KA^2)/(1/2 KA^2)`
`("K. E.")/(T. E.") = 8/18 xx 2/1`
`("K. E.")/(T. E.") = 8/9`
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