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Question: Answered & Verified by Expert
A simple harmonic motion is represented by $\alpha \frac{d^2 x}{d t^2}+\beta x=0$. Its period is
PhysicsOscillationsMHT CETMHT CET 2022 (10 Aug Shift 1)
Options:
  • A $\frac{2 \pi \beta}{\alpha}$
  • B $2 \pi \sqrt{\frac{\alpha}{\beta}}$
  • C $2 \pi \sqrt{\frac{\beta}{\alpha}}$
  • D $\frac{2 \pi \alpha}{\beta}$
Solution:
1731 Upvotes Verified Answer
The correct answer is: $2 \pi \sqrt{\frac{\alpha}{\beta}}$
The standard equation of SHM is: $\frac{d^2 x}{d t^2}=-\omega^2 x$
On comparing with equation: $\alpha \frac{d^2 x}{d t^2}+\beta x=0$
The angular frequency is given by: $\omega=\frac{\beta}{\alpha}$.
Therefore, the time period of SHM is:
$T=\frac{2 \pi}{\omega}=2 \pi \sqrt{\frac{\alpha}{\beta}}$

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