Question

If the total energy of a particle executing SHM is E, then the potential energy V and the kinetic energy K of the particle in terms of E when its displacement is half of its amplitude will be ________.

• A. $V=E/4$ and $K=3E/4$
• B. $V=3E/4$ and $K=E/4$
• C. $V=3E/4$ and $K=3E/4$
• D. $V=E/4$ and $K=E/4$

Hint:

At $x = A/2$, the potential energy is always $25%$ of total energy.

Answer 1

The Correct Option is A

Step 1: Concept
Total energy $E = \frac{1}{2}kA^{2}$. Potential energy $V = \frac{1}{2}kx^{2}$.
Step 2: Analysis
Given displacement $x = A/2$. $V = \frac{1}{2}k(A/2)^{2} = \frac{1}{4}(\frac{1}{2}kA^{2}) = E/4$.
Step 3: Calculation
Kinetic energy $K = E - V$. $K = E - E/4 = 3E/4$.
Step 4: Conclusion
Hence, $V=E/4$ and $K=3E/4$.
Final Answer:(A)