Question

For a simple pendulum, a graph is plotted between its kinetinc energy $\left(KE\right)$ and potential energy $\left(PE\right)$ against its displacement $x$. Which one of the following represents these correctly?
(graphs are schematic and not drawn to scale)

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

From formula,
In an SHM, variation of potential energy with displacement $x$ is given by
$PE=$$\frac{1}{2}k{x}^2$,
which represents the equation of a straight parabola with vertex at $x=0$.
And variation of kinetic energy with displacement $x$ is given by
$KE$$=\frac{1}{2}k(A^2-x^2)$,
which represents the equation of an inverted parabola with vertex at $x=A$.
Here $A$ is the amplitude of the SHM.
From both formula, we can say that a point at which $KE$ is maximum, potential energy will be minimum and that point will be at $x=0$
Hence, option (d) is the correct answer.

Why this question? Tips: In SHM, $KE$ at mean position = maximum $PE$ at extreme position = maximum and $KE+PE$ will be constant at every position.