JEE Mains · Physics · STD 11 - 13. oscillations
A particle is executing Simple Harmonic Motion \((SHM)\). The ratio of potential energy and kinetic energy of the particle when its displacement is half of its amplitude will be
- A \(1: 1\)
- B \(2: 1\)
- C \(1: 4\)
- D \(1: 3\)
Answer & Solution
Correct Answer
(D) \(1: 3\)
Step-by-step Solution
Detailed explanation
\(x =\frac{ A }{2}, \quad \text { P.E. }=\frac{1}{2} kx ^2\) \(K . E .=\frac{1}{2} kA ^2-\frac{1}{2} kx ^2\) \(\frac{ P . E }{ K . E }=\frac{ x ^2}{ A ^2- x ^2}=\frac{ A ^2}{4\left(\frac{3 A ^2}{4}\right)}=\frac{1}{3}\)
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