AP EAMCET · PHYSICS · Oscillations
For a particle executing simple harmonic motion, the displacement-time \((x-t)\) graph is as shown in the figure. The acceleration of the particle at \(t=\frac{4}{3} \mathrm{~s}\) is
- A \(-\frac{\sqrt{3}}{32} \pi^2 \mathrm{~cm} \mathrm{~s}^{-2}\)
- B \(\frac{32}{\sqrt{3}} \pi^2 \mathrm{~cm} \mathrm{~s}^{-2}\)
- C \(+\frac{\sqrt{3}}{32} \pi \mathrm{cm} \mathrm{s}^{-2}\)
- D \(+\frac{32}{\sqrt{3}} \pi \mathrm{cm} \mathrm{s}^{-2}\)
Answer & Solution
Correct Answer
(A) \(-\frac{\sqrt{3}}{32} \pi^2 \mathrm{~cm} \mathrm{~s}^{-2}\)
Step-by-step Solution
Detailed explanation
The displacement-time graph shown in the figure is a sine wave, so the equation of displacement, \(x=1 \sin \omega t\) Here, \(\quad T=8 \mathrm{~s}\) (for a complete cycle) Hence, \(\omega=\frac{2 \pi}{T}=\frac{2 \pi}{8}=\frac{\pi}{4} \mathrm{rad} / \mathrm{s}\) and…
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