Short Note

State an expression for K. E. (kinetic energy) and P. E. (potential energy) at displacement ‘x’ for a particle performing linear S.H. M. Represent them graphically. Find the displacement at which K. E. is equal to P. E.

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#### Solution

`:.K.E.=1/2mw^2(A^2-X^2)`

`P.E.=1/2mw^2X^2`

K.E. = P.E.

`1/2K(A^2-X^2)=1/2KX^2`

∴ A^{2}=2X^{2}

`:.X^2=A^2/2`

`:.X=A/sqrt2`

Concept: K.E.(Kinetic Energy) and P.E.(Potential Energy) in S.H.M.

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