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A particle of mas 10g is placed in a potential field given by` U=(500x^(2)+100)` erg `//` gm. Calculate the frequency of oscillation. |
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Answer» Potential energy of 10 gram particle is `U=10(50x^(2)+100)` erg. The force acting on the particle is given by `F=-(dU)/(dr)=-(d)/(dr)(500x^(2)+1000)` `=-1000x,` But `F=m(d^(2)x)/(dt^(2))` `:.m (d^(2)x)/(dt^(2))=-1000x or (d^(2)x)/(dt^(2))=-(1000x)/(m)` `=-(1000x)/(10)=-100x` As`(d^(2)x)/(dt^(2))=-omega^(2)x, so omega^(2)=100 or omega=sqrt(100)` Frequency of oscillation, `v=(omega)/(2pi)=(sqrt(100))/(2pi)=1.59s^(-1)` |
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