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Derive by method of dimensions an expres...

Derive by method of dimensions an expression for the energy (E ) of a body executing SHM assuming that this energy depends upon (i) the mass (m), (ii) the frequency (v) and the amplitude of vibration `(gamma)`.

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Let `E prop m^(a)v^(b)gamma^(c )`
`E=km^(a)v^(b)r^(c )`………………….(i)
Substituting the dimensional formulae of various quantities, we have `ML^(2)T^(-2)=M^(a)(T^(-1))^(b)L^(c )`
Comparing powers on both sides, we get `a=1, b=2, c=2`
Substituting the value of `a,b,c,` in equation (i) `E=km v^(2)r^(2)`.
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