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NEET 2007
Exam
NEET
Year
2007
Subject
Physics
Chapter
Oscillations

NEET 2007 · Physics · Oscillations

A particle executes simple harmonic oscillation with an amplitude a...

A particle executes simple harmonic oscillation with an amplitude aa. The period of oscillation is TT. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is:

Options

  1. AT/8T / 8
  2. BT/12T / 12
  3. CT/2T / 2
  4. DT/4T / 4.

Correct answer

B. T/12T / 12

Step-by-step solution

For equilibrium position x(t)=asin⁡ωtAt x(t)=a2∴sin⁡(π6)=sin⁡ωt{∵ω=2πT}or π6=2πtT⇒t=T12\begin{aligned} x(t) & =a \sin \omega t \\ \text{At } x(t) & =\frac{a}{2} \\ \therefore \sin \left(\frac{\pi}{6}\right) & =\sin \omega t\left\{\because \omega=\frac{2 \pi}{\mathrm{T}}\right\} \\ \text{or } \frac{\pi}{6} & =\frac{2 \pi t}{T} \\ \Rightarrow t & =\frac{T}{12} \end{aligned}
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