Question

The potential energy U(x) of a particle executing SHM is given by

• A. U (x) = k(x – a)²/2
• B. U(x) = k₁x + k₂x² + k₃x³
• C. U(x) = A e^−bx
• D. U(x) =constant

Answer 1

Answer: (A)

U (x) = k(x – a)²/2

Answer 2

F=$- \frac{dU}{dx}$For U(x)=$\frac{k}{2}$ (x–a)² $\frac{dU}{dx} = k(x - a)$

⇒ F = -k(x – a)

This is the condition for SHM about point x =+ a

Other functions do not satisfy this condition.

Hence Answer is (1)