The potential energy (U) of a particle executing simple harmonic motion, where k is a constant and x is displacement, is _________.

CONCEPT:

• Simple Harmonic Motion (SHM): Simple harmonic motion is a special type of periodic motion or oscillation where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement.
  • Example: Motion of an undamped pendulum, undamped spring-mass system.

The potential energy (U) of a particle in simple harmonic motion is given by the formula:

\({\rm{U}} = \frac{1}{2}{\rm{k}}{{\rm{x}}^2}\)

Where, x = Distance from its mean position and k = spring constant.

EXPLANATION:

• The potential energy (U) of a particle executing simple harmonic motion, where k is a constant and x is displacement, is 0.5kx². So option 1 is correct.

EXTRA POINTS:

Velocity in simple harmonic motion: The relation  between velocity and the displacement can be given as:

\({\rm{V}} = {\rm{\omega }}\sqrt {{A^2} - {y^2}} \),

Where V = velocity, ω = angular velocity, A = amplitude and y = displacement.

Kinetic energy (KE) = ½ m V2

Total mechanical energy (TE) = \( \frac{1}{2}{\rm{k}}{{\rm{A}}^2}\)