MHT CET · Physics · Oscillations
The periodic time of a particle doing simple hormonic motion is \(4 \mathrm{~s}\). The time taken by it to go from its mean position to half the maximum displacement (amplitude) is
- A \(2 \mathrm{~s}\)
- B \(1 \mathrm{~s}\)
- C \(\frac{2}{3} \mathrm{~s}\)
- D \(\frac{1}{3} s\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{3} s\)
Step-by-step Solution
Detailed explanation
\(y=A \sin \left(\frac{2 \pi}{T}\right) t\)
\(
\begin{array}{ll}
\Rightarrow & \frac{A}{2}=A \sin \left(\frac{2 \pi}{4}\right) t \\
\Rightarrow & \frac{\pi t}{2}=\frac{\pi}{6} \\
\Rightarrow & t=\frac{1}{3} \mathrm{~s}
\end{array}
\)
\(
\begin{array}{ll}
\Rightarrow & \frac{A}{2}=A \sin \left(\frac{2 \pi}{4}\right) t \\
\Rightarrow & \frac{\pi t}{2}=\frac{\pi}{6} \\
\Rightarrow & t=\frac{1}{3} \mathrm{~s}
\end{array}
\)
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