Question

For the particle executing SHM the displacement $x$ is given by $x=A\cos \omega t$. Identify which represents variation of potential energy as a function of time $t$ and displacement $x$

• A. I,III
• B. II,IV
• C. II,III
• D. I,IV

Answer 1

The correct option is A I,III

Displacement of the particle is given as $x=Acoswt$

Potential energy $U=\frac{1}{2}k{x}^2$

Thus $U$ Vs $x$ graph is an upward parabola as represented by $III$

Also $U=\frac{1}{2}k{x}^2=\frac{1}{2}k{A}^{2}co{s}^{2}wt$

Hence, $I$ represents the variation of potential energy as a function of time.