JEE Mains · Physics · STD 11 - 13. oscillations
A particle starts simple harmonic motion from the mean position. Its amplitude is \(a\) and total energy \(E\). At one instant its kinetic energy is \(3E/4.\) Its displacement at that instant is
- A \({y}={a}\)
- B \(y=\frac{a}{2}\)
- C \(y=\frac{a \sqrt{3}}{2}\)
- D \(y=\frac{a}{\sqrt{2}}\)
Answer & Solution
Correct Answer
(B) \(y=\frac{a}{2}\)
Step-by-step Solution
Detailed explanation
(b) \(\frac{K}{E} = \frac{{\frac{1}{2}m{\omega ^2}({a^2} - {y^2})}}{{\frac{1}{2}m{\omega ^2}{a^2}}}\) \(= \frac{{{a^2} - {y^2}}}{{{a^2}}} \) \(= 1 - \frac{{{y^2}}}{{{a^2}}}\) So, \(\frac{{\left( {\frac{{3E}}{4}} \right)}}{E} = 1 - \frac{{{y^2}}}{{{a^2}}}\)…
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