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At what displacement, (i) the P.E. of a simple harmonic oscillator is maximum, (ii) the K.E. is maximum?

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The P.E. of a particle executing S.H.M. is given by:

\(E_P=\frac{1}{2}m\omega^2y^2.\)

EP is maximum when y = r = amplitude of vibration, i.e., the particle is passing from the extreme position and is minimum when y = 0, i.e., the particle is passing from the mean position.

The K.E. of a particle executing S.H.M. is given by;

\(E_k=\frac{1}{2}m\omega^2(r^2\,-\,y^2)\)

EK is maximum when y = 0, i.e., the particle is passing from the mean position and EK is minimum when y = r, i.e., the particle is passing from the extreme position.

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