ExamBro
ExamBro
MHT CET · Physics · Oscillations

A particle executes simple harmonic motion with amplitude 'A' and period \({ }^{\prime} \mathrm{T}^{\prime}\). If it is half way between mean position and extreme position, then its speed at that point is

  1. A \(\frac{3 \pi \mathrm{A}}{\mathrm{T}}\)
  2. B \(\frac{\sqrt{3} \pi \mathrm{A}}{2 \mathrm{~T}}\)
  3. C \(\frac{\pi \mathrm{A}}{\mathrm{T}}\)
  4. D \(\frac{\sqrt{3} \pi A}{\mathrm{~T}}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{\sqrt{3} \pi A}{\mathrm{~T}}\)

Step-by-step Solution

Detailed explanation

\(v=\omega \sqrt{\left(A^{2}-x^{2}\right)}=\frac{2 \pi}{T} \sqrt{A^{2}-\frac{A^{2}}{4}}=\frac{\sqrt{3} A}{2} \times \frac{2 \pi}{T}\)
\(=\frac{\sqrt{3} \pi \mathrm{A}}{\mathrm{T}}\)