For a simple pendulum, a graph is plotted between its Kinetic Energy (KE) and Potential Energy (PE) against its displacement d. Which one of the following represents these correctly? (graphs are schematic and not drawn to scale)

Question

For a simple pendulum, a graph is plotted between its Kinetic Energy (KE) and Potential Energy (PE) against its displacement d. Which one of the following represents these correctly? (graphs are schematic and not drawn to scale) (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Taking minimum potential energy at mean position to be zero,
the expression of KE and PE are

K E = \frac{1}{2} mω;^{2} (A^{2} - d^{2})

and

PE = \frac{1}{2} mω;^{2} d^{2}

Both graphs are parabola. At

d = 0

,
the mean position

PE = 0

and

K E = \frac{1}{2} m ω^{2} A^{2}

=maximum
At

d = \pm; A,

the extreme positions,

K E = 0

and

PE = \frac{1}{2} m ω^{2} A^{2}

=maximum
Therefore, the correct graph is (a).

Q. For a simple pendulum, a graph is plotted between its Kinetic Energy (KE) and Potential Energy (PE) against its displacement d. Which one of the following represents these correctly? (graphs are schematic and not drawn to scale)

Q. For a simple pendulum, a graph is plotted between its Kinetic Energy $(K E)$ and Potential Energy $(PE)$ against its displacement d. Which one of the following represents these correctly? (graphs are schematic and not drawn to scale)