TS EAMCET · Physics · Oscillations
If the displacement \((x)\) and velocity \((v)\) of a particle executing simple harmonic motion are related through the expression \(4 v^2=25-x^2\), then time period is
- A \(\pi\)
- B \(2 \pi\)
- C \(4 \pi\)
- D \(6 \pi\)
Answer & Solution
Correct Answer
(A) \(\pi\)
Step-by-step Solution
Detailed explanation
\[ 4 v^2=25-x^2 \] Differentiating both the side \[ \begin{aligned} 4(2 v) \frac{d v}{d t} & =0-2 x \frac{d x}{d t} \\ \frac{d v}{d t} & =A \text { (acceleration) } \\ \frac{d x}{d t} & =v \text { (velocity) } \end{aligned} \]…
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