Question

The potential energy of a particle with displacement x is U(x). The motion is simple harmonic. If k is a positive constant then

• A. $U=kx$
• B. $U=k$
• C. $U=-k{x}^2/2$
• D. $U=k{x}^2$

Answer 1

The correct option is D $U=k{x}^2$

We know that potential energy $U\left(x\right)$ is directly proportional to the square of the displacement $\left(x^2\right)$ from the mean position i.e.
$U\left(x\right)\propto x^2\Rightarrow U\left(x\right)=k{x}^2$