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When the displacement is one half of the amplitude, what fraction is potential in SHM ? At what displacement is the energy half kinetic and half potential? |
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Answer» Fraction of total energy which is kinetic `=(K.E.)/(T.E.)` `=((1)/(2)momega^(2)(a^(2)-y^(2)))/((1)/(2)m omega^(2)a^(2))=(a^(2)-y^(2))/(a^(2))=(a^(2)-(a^(2))/(4))/(a^(2))=(3)/(4)` Fraction of total energy which is potential `=(P.E.)/(T.E.)=((1)/(2)momega^(2)y^(2))/((1)/(2)momega^(2)a^(2))=(y^(2))/(a^(2))=(a^(2)//4)/(a^(2))=(1)/(4)` KE `=` PE `(1)/(2)momega^(2)(a^(2)-y^(2))=(1)/(2)momega^(2)y^(2)` On solving , `y=a//sqrt(2)` |
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