1. Tardigrade
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  4. Assertion: The graph of potential energy and kinetic energy of a particle in SHM with respect to position is a parabola. Reason: Potential energy and kinetic energy do not vary linearly with position.

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Q. Assertion : The graph of potential energy and kinetic energy of a particle in SHM with respect to position is a parabola.
Reason : Potential energy and kinetic energy do not vary linearly with position.

AIIMSAIIMS 2016Oscillations

Solution:

Both assertion and reason are true but reason is not the correct explanation of assertion.
$P.E.=\frac{1}{2}m\omega^{2}y^{2}$ and $K.E.=\frac{1}{2}m\omega^{2}\left(a^{2}-y^{2}\right).$
The variation of both potential energy and kinetic energy is proportional to $y^2$. Therefore displacement versus P.E. or K.E. graph is a parabola (because parabolic equation is $z = 4au^2$).