Question

The potential energy of a particle \( U(x) \) executing simple harmonic motion is given by:

• A. \( U(x) = \frac{k}{2} (x - a)^2 \)
• B. \( U(x) = k_1 x + k_2 x^2 + k_3 x^3 \)
• C. \( U(x) = A e^{-bx} \)
• D. \( U(x) = {a constant} \)

Hint:

For SHM:
- Potential energy is quadratic in displacement.
- \( U(x) \) is minimum at equilibrium and increases as \( x \) moves away.
- Total energy is conserved: \( E = KE + PE \).

Answer 1

The Correct Option is A

Step 1: The potential energy of a simple harmonic oscillator is given by:
\[ U(x) = \frac{1}{2} k x^2 \]
Step 2: Comparing with the given options, option (A) correctly represents the potential energy form in SHM.