AP EAMCET · PHYSICS · Oscillations
For a particle executing simple harmonic motion, the ratio of kinetic and potential energies at a point where displacement is one half of the amplitude is
- A \(3: 1\)
- B \(1: 3\)
- C \(2: 1\)
- D \(1: 2\)
Answer & Solution
Correct Answer
(A) \(3: 1\)
Step-by-step Solution
Detailed explanation
\(KE = \frac{1}{2}m\omega^2(A^2 - x^2)\) \(PE = \frac{1}{2}m\omega^2 x^2\) \(x = A/2\) \(\frac{KE}{PE} = \frac{\frac{1}{2}m\omega^2(A^2 - (A/2)^2)}{\frac{1}{2}m\omega^2 (A/2)^2}\) \(\frac{KE}{PE} = \frac{A^2 - A^2/4}{A^2/4} = \frac{3A^2/4}{A^2/4}\) \(\frac{KE}{PE} = 3:1\)
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