Question

For a particle performing simple harmonic motion, when displacement is \( x \), the potential energy and restoring force acting on it is denoted by \( E \) and \( F \) respectively. The relation between \( x \), \( E \), and \( F \) is

• A. \( \frac{E}{F} + x = 0 \)
• B. \( \frac{2E}{F} + x = 0 \)
• C. \( \frac{E}{F} - x = 0 \)
• D. \( \frac{2E}{F} - x = 0 \)

Hint:

In SHM, use the relations between displacement, force, and energy to solve for the unknown quantities.

Answer 1

The Correct Option is B

Step 1: Relation for SHM.
For a particle undergoing simple harmonic motion (SHM), the potential energy \( E \) and restoring force \( F \) are related by the equation: \[ E = \frac{1}{2} k x^2 \] and \[ F = -k x \] where \( k \) is the spring constant.
Step 2: Relating \( E \), \( F \), and \( x \).
By substituting \( F = -k x \) into the equation for \( E \), we get: \[ \frac{2E}{F} = x \]
Step 3: Conclusion.
Thus, the correct answer is (B) \( \frac{2E}{F} + x = 0 \).